Completing the square

Question

In Algebra 2, I am given the following equation:

 

3x² - 3 = 3x

 

I am told to solve by completing the square.

Answer 1

3x² - 3 = 3x

First of all, to simplify, you can divide the equation by 3

x² - 1 = x

Now, bring x on the same side as x² and move 1 on the other side

x²-x = 1

To make the left hand side a complete square, take half of the x coefficient and square it, i.e (-1/2)² = 1/4

and add this number to both sides of your equation

x²-x+1/4 = 1+1/4

(x-1/2)² = 5/4

Square root both sides

x-1/2 = ±√5/2

x = 1/2 ± √5/2

x = (1±√5)/2

Answer 2

3x² - 3x - 3 = 0

3(x² - x - 1) = 0

x² - x         -1 = 0

x² - x             = 1

x² - x + (0.5)² = 1 + (0.5)²

(x - 0.5)² = 1.25

(x - 0.5)² = 5/4

x - 0.5 = (±√5)/2

x = (1 ± √5) / 2