How do you solve x^2-12x=-28 by completing the square?

1 Answer
EZ as pi
Sep 3, 2016

x =8.828 or x = 3.172

Explanation:

(x+- p)^2 = x^2 +-2px + p^2

If you have the correct combination of 3 terms, you can write the expression as (x+-p)^2
Add the correct last term each time, to 'complete the square.'

x^2 color(blue)(-12)x + square = -28 " "square = (color(blue)(-12)/2)^2 = color(red)(36)
x^2 color(blue)(-12)x + color(red)(36) = -28 +color(red)(36)

(x-6)^2 = 8 " " -6 = color(blue)(-12)/2

x- 6 = +-sqrt8

x = sqrt8+6 =8.828 " or " x = -sqrt8+6 =3.172

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