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