Question

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

Answer 1

`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`