4x^2 – 5x – 12 = 0 : Quadratic equations are like a key that can unlock exciting adventures in math. In this blog, we will focus on solving a specific equation, 4x^2 – 5x – 12 = 0. Quadratic equations are important in different areas of science and math. So, let’s get started and learn how to solve this equation and how it can help us understand things better.

A quadratic equation is a math problem that has an x squared term in it. It’s like a puzzle that we have to solve using math.

Simply put, quadratic equations are math problems with variables that are squared.

This is a special math equation that has three numbers in it: a, b, and c. The equation looks like this: a times x squared plus b times x plus c equals zero.

Let’s say we have some numbers called a, b, and c, and a special letter called x. We want to figure out what value of x will make an equation true.

Also Read: x*x*x is equal to 2 : Comprehensive Guide to solve and Prove it

Overview of 4x^2 – 5x – 12 = 0 quadratic equations

In the equation 4 times a number squared minus 5 times the same number minus 12 equals zero, the numbers that are multiplied by the variables are called coefficients.

A is equal to 4, B is less than 5, and C is equal to negative ( 4x ^ 2 – 5x – 12 = 0)

When we change around this math problem, we can see that it looks like a special kind of math problem called a quadratic equation.

A quadratic equation is like a special math puzzle. It has a special shape that looks like a U or an upside-down U. It always has a variable squared, which means that the number is multiplied by itself. Quadratic equations can have different numbers and symbols, but they always follow the same pattern.

Quadratic equations have special traits that are important for understanding and solving them. These traits help us figure out how to solve the equations.

A quadratic equation is like a curved line that looks like a U or an upside-down U. The point at the very bottom or top of the curve is called the vertex. The curve is also the same on both sides, so it looks the same if you flip it.

By understanding these traits, we can learn more about how they act and how they can be used in the real world.

Method of solving Quadratic 4x^2 – 5x – 12 = 0 Equation

By following these steps and doing some calculations, we can find the two solutions to this equation.

There are different ways to find the answer to the math problem 4 times x squared minus 5 times x minus 12 equals 0. We are going to learn about two of these ways.

1. Quadratic Formula:

Quadratic formula

This is a special formula that helps us find the solutions to a math problem involving quadratic equations. It looks like this: (-b ± √(b^2 – 4ac)) / 2a. Factoring Method: This is a way to break down a math problem into smaller pieces to make it easier to solve.

Now, let’s look at each of them so we can understand them better.

2. Factoring Method

Factoring method is a way to break down a number into smaller numbers that can be multiplied together to get the original number.

You can only use the factoring method when the equation can be broken down into smaller parts. This method helps you solve the equation by finding those smaller parts and solving them one by one.

To find the answer to the equation 4 times a number squared minus 5 times the number minus 12 equals zero, you need to figure out what two groups of numbers can be multiplied together to get the equation.

This equation can be written as two smaller equations: 2 times some number plus 3 times some number equals 0, and 2 times some number minus 4 times some number equals 0.

If we make each part equal to zero, we get two problems to solve: 2x + 3 = 0 and 2x – 4 = 0.

When you figure out these two math problems, you will know what number x is equal to. The answer is x= -3/2 and x=2.

The quadratic formula is a special equation that helps us find the answer to certain math problems. It is like a magic formula that tells us how to solve equations that have x^2 (x squared) in them. It has three parts – a, b, and c – that we need to know to use the formula. Once we plug in these numbers, the formula will give us the answer to our math problem. It’s like a secret code that helps us solve tricky equations!

The quadratic formula is a special way to find the answers to math problems called quadratic equations. It is a very important formula because it can always give us an answer, even if the problem seems tricky and hard to solve.

We have a special formula that helps us solve this equation. The equation has some numbers and a letter called x. We want to find the value of x that makes the equation true. The formula helps us do that.

This formula helps us find the value of x in a math problem. We use it when we have numbers for a, b, and c. The formula helps us figure out what x equals by plugging in those numbers.

This is a way to write down a rule or equation that helps us solve problems or understand how things work. It shows us how different parts or numbers are connected to each other.

There are three numbers: 4, -5, and -12.

Once we put this into the formula, we can easily figure out the answers for x.

After doing some math, we figured out that x is either -1.5 or 2.

Real World Applications

Real world applications mean using something in real life, like using math to measure how tall a building is or using science to cook food.

Quadratic equations are math problems that are used in different areas like economics, engineering, and physics. They help solve real-life situations like building things, studying motion, and understanding how objects fly through the air.

Conclusion

The conclusion is like the ending of a story or the final part of something. It is when we sum up or wrap up everything that we have talked about or done. It helps us understand the main points or ideas and gives us a sense of closure.

We have been studying a math problem called a quadratic equation. It looks like this: 4x^2 – 5x – 12 = 0. We learned two different ways to solve this problem: one is called factoring and the other is called the quadratic formula. By using these methods, we were able to find the answer for x. Understanding quadratic equations is really useful because it helps us solve many different kinds of math problems.

FAQ: 4x^2 – 5x – 12 = 0

What is a Quadratic Equation?

A quadratic equation is a special kind of math problem that has a variable (like x) raised to the power of 2 (squared). It’s like a puzzle where we need to find the value of the variable that makes the equation true.

Who is called the person who first discovered and created the quadratic equation?

Muhammed ibn Musa al-Khwarizmi was a smart person who lived a long time ago and did important math work.

Solving math problems like 58: 2x^2 – 9x^2; 5 – 3x + y + 6 can be tricky, but it’s an important skill to learn. In this article, we’ll go through the steps of solving this equation one by one. We’ll learn different ways to make it simpler and figure out the values of ‘x’ and ‘y’ that make the equation true. By the end of the article, you’ll feel more confident about solving equations and be ready to tackle more challenging problems.

Both equations are ways of showing relationships between numbers. We can use them to solve problems and find out what the values of x and y are.

Also Read: Solution of x*x*x is equal to 2 Equation

Know all about 58: 2x^2 – 9x^2; 5 – 3x + y + 6 Education

Before we solve the problem, let’s look at the equation closely: 58 divided by (2 times x squared minus 9 times x squared) equals 5 minus 3 times x plus y plus 6. This equation has three different parts: 2x squared, -9x squared, and 5 minus 3x plus y plus 6. Our goal is to find the values of ‘x’ and ‘y’ that make this equation true.

Combining terms

Combining like terms means putting together numbers or variables that are the same. It’s like grouping things that are alike to make math problems easier to solve.

We need to make the equation simpler. We have two terms that have x^2, which are 2x^2 and -9x^2. When we put them together, we get -7x^2. The equation now looks like this: 58: -7x^2; 5 – 3x + y + 6.

Isolating Variables

Isolating ‘x’ means separating ‘x’ from the other numbers or letters in the equation so we can solve for its value.

Solitude ‘x’

To keep working on finding the numbers for ‘x,’ we want to make it all by itself on one side of the problem. We’ll move any parts with ‘x’ to the left and the numbers that don’t have ‘x’ to the right.

Solitude ‘y’

There are some numbers and letters in this equation. If we solve it, we can find the value of the letter y.

Keeping ‘y’ by itself or separating ‘y’ from the other numbers or variables.

To find out what ‘y’ is, we have to make sure it’s all by itself on one side of the math problem.

Solution Using the Quadratic Formula

After we have squared the “x” number, we need to multiply it by 7. Finally, we subtract this result from the original 58. To make this easier for a child to understand, we can break it down into smaller steps. So, in simpler terms, the equation is telling us to take the number 58, subtract the sum of 5 and 6, and then subtract the result of multiplying 7 by the square of a number “x”. First, we have the number 58. Then, we need to do some calculations. We need to add 5 and 6 together, which equals 11. Next, we need to multiply this 11 by another number, which is represented by the “x” in the equation. Lastly, we need to square this “x” number, which means multiplying it by itself.

The Quadratic Formula is like a special tool that helps us find the answer to math problems with quadratic equations. It’s like a magical formula that tells us the values of x when we have a quadratic equation.

x = (-b ± √(b^2 – 4ac)) / 2a

Since there is a special term in the equation (-7x^2), we can use a special formula to find the answers for ‘x’. This formula helps us figure out the values of ‘x’ in the equation ax^2 + bx + c = 0.

This is a formula to find the value of x in a math problem. It involves using numbers called a, b, and c to solve for x.

Let’s say we have a problem where we need to find the value of something. In this problem, we have three numbers: -7, 0, and a number that we don’t know yet. We can put these numbers into a special formula called the quadratic formula to find the answer. When we do that, we will get the value of the unknown number.

x = (± √(0 – 4*(-7)(58 – (5 + 6) + y))) / 2(-7)

Checking the solutions means making sure the answers are correct.

After figuring out the numbers for ‘x’, it’s important to double check them by putting them back into the original problem. This way we can make sure we got the right answer.

A graphical representation is a picture or drawing that shows information in a visual way.

Another way to find the answers is by drawing a picture of the equation on a graph. We can see where the line crosses the x-axis to figure out the solutions for ‘x.’ This also helps us understand how the equation works.

The end or final result.

Solving equations 58: 2x^2 – 9x^2; 5 – 3x + y + 6 is important and can be used in lots of different types of math. In this article, we figured out the answer to a tricky 58: 2x^2 – 9x^2; 5 – 3x + y + 6 equation by using different ways to solve it. Learning these methods can help you solve other equations too.

Let’s learn about something called quadratic equations x²-11x+28=0, which are a type of math problem. We will focus on one specific equation called x²-11x+28=0. We’ll talk about what quadratic equations are, different ways to solve them, and how they can be used in real life.

A quadratic equation is a math problem that includes an x-squared term, an x term, and a constant term. It looks like this: x²-11x+28=0.

To embark on this journey, we must first understand the essence of the quadratic equation. A quadratic equation is a quadratic polynomial equation, characterized by a quadratic variable. The basic form of the quadratic equation is expressed as follows:

Complete Overview about Quadratic Equations x²-11x+28=0

This is a math equation with three terms that we’re trying to solve.

This math problem has some letters and numbers. The letters ‘a,’ ‘b,’ and ‘c’ are like special numbers called coefficients. The letter ‘x’ is a special letter that can be any number. The equation x²-11x+28=0 is a fancy way to write a math problem.

ax^2 + bx + c = 0

What is General Form of a Quadratic Equation?

The general form of a quadratic equation is an equation that looks like ax^2 + bx + c = 0. It’s like a math puzzle with three pieces that we need to solve.

Knowing the general shape of a quadratic equation is really important because it helps us understand how these equations work. When we look at a specific equation, we can easily find the numbers called coefficients, like ‘a,’ ‘b,’ and ‘c.’ In this particular equation, ‘a’ is 1, ‘b’ is -11, and ‘c’ is 28.

To solve the equation x²-11x+28=0, we need to find the value of x that makes the equation true.

Quadratic equations are math problems that can be solved in different ways. Let’s look at two popular Two methods to solve them.

Solution By Factoring

Factoring is like taking apart a puzzle or breaking down a big number into smaller pieces.

Factoring is a way to solve certain math problems by breaking them down into smaller pieces. But for really tricky problems like x²-11x+28=0, factoring might not work very well.

By Quadratic Formula x^2-11x+28=0

The quadratic formula is a special math equation that helps us find the solutions to problems involving quadratic equations. It helps us figure out the values of variables in these types of equations.

The quadratic formula is a special math equation that helps us solve problems involving quadratic equations. It can be used in many different situations and is very helpful.

To find the value of x in an equation, you can use this formula: negative b plus or minus the square root of b squared minus 4 times a times c, all divided by 2 times a.

This formula helps us find the special numbers for ‘x’ that make the equation equal to zero.

Solve this problem

To solve this problem, we can imagine a story where we have a shape called a quadratic. This shape has a special formula that helps us find the value of x. In our story, the quadratic is like a puzzle, and we need to solve it to find the missing piece. To solve this, we can use a special method called factoring. We can break down the quadratic into two parts that, when multiplied together, give us the original equation. In our story, it’s like splitting the puzzle into two smaller pieces that fit together perfectly. The equation tells us that the quadratic has two parts: x squared, 11 times x, and 28. We want to rearrange the equation to make it easier to solve. So, we can move the 28 to the other side of the equation, like moving a piece of the puzzle to a different spot. By solving these equations, we find that x can be either 4 or 7. These are the missing numbers that complete the puzzle and make the quadratic equation true. By using factoring, we find that the two smaller pieces are (x minus 4) and (x minus 7). When we multiply these two pieces together, we get the original equation: (x minus 4) times (x minus 7) equals 0. So, in the end, we have solved the math problem by imagining a story about a quadratic puzzle. We used factoring to break down the puzzle into smaller pieces and found the missing numbers to complete it. Now, we have x squared minus 11 times x equals negative 28. This is like saying that the quadratic is missing a piece that is equal to negative 28. We want to find what numbers x could be to complete the puzzle. Let’s imagine we have a math problem that we want to solve. The problem is written like this: x squared minus 11 times x plus 28 equals 0. We want to find out what number x is in order to make this equation true. Now, we can solve for x by setting each of the smaller pieces equal to 0. This means that either (x minus 4) equals 0 or (x minus 7) equals 0. In our story, it’s like finding the missing numbers that make each small piece equal to zero.

x^2-11x+28=0: A Case Study

Now, let’s look at the equation x squared minus 11x plus 28 equals 0. We will break it down and solve it using a special formula.

Step 1 : we need to find the numbers that are in front of the letters in an equation. These numbers are called coefficients. To start this journey, we need to figure out the numbers in the equation. In this equation, ‘a’ is 1, ‘b’ is -11, and ‘c’ is 28.

Step 2 : is all about using a special formula called the Quadratic Formula to solve a quadratic equation. A quadratic equation is like a puzzle that has an “x” and numbers in it.

x = (-(-11) ± √((-11)^2 – 4 * 1 * 28)) / (2 * 1)

The Quadratic Formula helps us figure out what number “x” is. It’s like using a special tool to solve the puzzle and find the hidden answer.

Now that we have the coefficients under control, we can move on to applying the quadratic formula. The equation takes shape as follows:

To find the answer to a math problem, we can use a formula called the quadratic formula. The formula helps us solve equations with variables.

When we try to find an answer, we make the math problem easier by changing it a little.

To find x, you add 11 to the square root of (121 minus 112), and then divide the result by 2.

x = (11 ± √(121 – 112)) / 2

x = (11 ± √9) / 2

Step 3 is about finding the roots. Roots are the numbers that, when you multiply them together, give you the original number. It’s like finding the secret numbers that make a special math equation work.

As we figure out the math problem, we find two possible answers.

Our first equation says that if we add 11 and 3 together and then divide by 2, the answer is 7. The second equation says that if we subtract 3 from 11 and then divide by 2, the answer is 4.

This equation has two answers: 7 and 4 when you solve it.

1. x = (11 + 3) / 2 = 7
2. x = (11 – 3) / 2 = 4

Graphical representation of quadratic equations

A graphical representation of quadratic equations is like drawing a picture to show how numbers can change. It helps us understand how things can go up and down in a certain pattern.

In quadratic equations, we often use a U-shaped curve called a parabola to help us understand what the equation is doing. The middle point of the curve is really important because it tells us the highest or lowest point of the curve.

Different ways we can use quadratic equations in real life.

Quadratic equations are not just something we learn in school, they are actually very useful in many different areas like science, building things, and money. In these real-life situations, quadratic equations help us solve problems accurately and find the best solution.

conclusion

In simple words, the conclusion is like the ending or final part of something. It’s when we wrap up everything that we have talked about or done and come to a final decision or understanding. It’s like the last piece of a puzzle that helps us see the bigger picture and know what it all means.

In simple terms, we have learned a lot about quadratic equations. We found out how to solve them using a special formula and saw how they can be useful in real life. We also looked at pictures of quadratic equations called parabolic graphs.