Completing the Square Assignment

Question

1. Solve x² - 6x = -8 by completing the square. Enter each step.



2. Solve 4x² - 12x + 7 = 0 by completing the square. Enter each step.

Answer 1

Hello, Haya!

Okay, for question 1:

x² - 6x = -8

Since it's not already a perfect square you must complete the square.

First, you need to take the -6 coefficient and divide it by 2 and then square it. It will then be ( -3)² which is 9.

Then you need to add that number to both sides of the equation.

x² - 6x +9 = -8 +9

Now you can write it as a perfect square:

(x - 3)² = 1

Now, to solve the equation you need to take the square root of both sides and you will see that

x - 3 = ± 1

x = 3 ±1

x = 4 and x = 2 are your answers.

For question 2:

4x² - 12x + 7 = 0

It is easiest to divide the equation by 4 to get rid of the first coefficient (the 4)

So, if you divide both sides by 4 you get:

x² - 3x + 7/4 = 0

x² - 3x = -7/4

Now, you need to complete the square again. So you will need to take half of the -3 and square it, which is

(-3/2)² which is 9/4

So you can now add it to both sides.

x² - 3x + 9/4 = -7/4 + 9/4

Now you can write as a square:

(x - 3/2)² = 2/4 = 1/2

Now, take the square root of both sides:

x - 3/2 = ± √(1/2) or you can write this as √2/2

x = 3/2 ± √2⁄2

So, x = (3+√2)⁄2 or (3-√2)⁄2