## Completing the square:

Completing the square is a term used to describe putting an equation into x^2 + bx form. This is accomplished by adding (b/2)^2 to x + bx to get x + bx + (b/x)^2, and always remember to add it to both sides. For example,

Solve x^2 - 12x + 4 = 0 by completing the square:

First, subtract 4 from each side to get:

x^2 - 12x = -4

Then add (b/2)^2 to BOTH SIDES of the equation to get:

x^2 - 12x + 36 = -4 + 36

Then factor the trinomial to get:

(x - 6)^2 = 32

Find the square root:

x - 6 = (+/-) √32

Add 6 to both sides:

x = 6 (+/-) √32

Simplify to get an answer of:

x = 6 (+/-) 4√2

Solve x^2 - 12x + 4 = 0 by completing the square:

First, subtract 4 from each side to get:

x^2 - 12x = -4

Then add (b/2)^2 to BOTH SIDES of the equation to get:

x^2 - 12x + 36 = -4 + 36

Then factor the trinomial to get:

(x - 6)^2 = 32

Find the square root:

x - 6 = (+/-) √32

Add 6 to both sides:

x = 6 (+/-) √32

Simplify to get an answer of:

x = 6 (+/-) 4√2