Question

1. # Solve X2 = 12X – 15 By Completing The Square. Which Is The Solution Set Of The Equation?

If you’ve ever been stumped by a math problem, you know how frustrating it can be. But while some equations seem impossible, they actually have solutions. That’s why the process of completing the square is such an important one—it allows us to solve equations that would otherwise remain unsolvable. In this article, we will look at an example of solving x2 = 12x – 15 by completing the square, and come up with the solution set of the equation. Along the way, we will discuss key concepts like how to complete the square and how to determine what the solution set of an equation is. So if you’re interested in getting a better understanding of completing the square and finding a solution set for an equation, read on!

## What is solving by completing the square?

In mathematics, solving by completing the square is a technique used to solve quadratic equations. The general form of a quadratic equation is ax^2 + bx + c = 0. To solve by completing the square, one first rearranges the equation into what is known as the quadratic equation in standard form: ax^2 + bx = -c. Next, one calculates what is known as the discriminant, which is equal to b^2 – 4ac. The discriminant can be used to determine the number and type of solutions that the equation has. If the discriminant is positive, then there are two real solutions. If the discriminant is negative, then there are no real solutions. Finally, if the discriminant is equal to zero, then there is only one solution. To find the solutions, one simply completes the square on both sides of the equation and then solves for x.

## How to solve X2 = 12X – 15 by completing the square

To solve x2 = 12x – 15 by completing the square, we need to first determine what value goes in the empty box. To do this, we take half of the coefficient of x, which is 6, and square it. This gives us 36. We then add this to both sides of the equation to get:

x2 + 36 = 12x – 15 + 36

x2 + 36 = 12x + 21

Now we have a perfect square on the left side of the equation. To finish solving, we take the square root of both sides:

√(x2 + 36) = √(12x + 21)

x+6=√(12x+21)

And that’s it! We have now solved for x by completing the square.

## The solution set of the equation

The set of solutions to an equation is the set of values that make the equation true. In this case, the equation is X = X – by completing the square. The solutions to this equation are all the values of X that make the equation true.

To find the solution set of this equation, we need to first understand what it means to complete the square. Completing the square is a process by which we take an algebraic expression and rewrite it in such a way that all terms are squared. For example, consider the expression x2 + 5x + 6. We can rewrite this expression as (x2 + 5x + 6) = (x + 2)2 – 4. Notice that in this new form, all terms are squared. This is what it means to complete the square.

Now that we understand what it means to complete the square, let’s go back to our original equation and use this process to solve it. We start with our original equation: X = X – by completing the square. To solve this equation, we need to rewrite it so that all terms are squared. We do this by adding a constant to both sides of the equation: X + c = (X – c)2 . Now all terms are squared on both sides of the equality sign and we can solve for X .

We solve this equation by taking the square root of both sides: √(X+c) = √((X-c)2). Solving for X, we get X = c.

Therefore, the solution set of this equation is all values of c that make the equation true. In this case, any real number can be a solution to this equation since it is always true no matter what value of c is chosen. Therefore, the solution set is {all real numbers}.

## Conclusion

In conclusion, completing the square is an effective way to solve equations such as x2 = 12x – 15. By following the steps outlined in this article, you can find the solution set of {3,5}. Solving equations by completing the square is a useful skill that can be applied in many different real-world situations. With practice and patience, anyone can become proficient at solving these types of problems using this method.

2. ‍ Have you ever been stuck trying to solve an equation like X2 = 12X – 15? It can be a daunting task, but don’t worry- it’s not as hard as it looks! Completing the square is a great way to solve equations like this, and it’s not as difficult as it might seem.

What Is Completing The Square? Completing the square is a mathematical process used to solve quadratic equations. It involves breaking down the equation into two parts and solving the equation by adding or subtracting a number to both sides. In this case, the number to be added or subtracted is the coefficient of the X2 term.

How Do I Do It? To solve the equation X2 = 12X – 15 by completing the square, you must first factor out the X2 term. This is done by multiplying both sides of the equation by 4, which gives you 4X2 = 48X – 60.

Next, you must add or subtract the coefficient of the X2 term, which is 4. Since the equation is negative, subtracting 4 from both sides gives you 4X2 – 4 = 48X – 64.

Finally, you must divide both sides by 4 and take the square root of both sides, which gives you X = 8 ± √60. This is the solution set of the equation.

Congratulations! You have successfully solved the equation X2 = 12X – 15 by completing the square. Now you know how to solve equations like these with ease!