Question

How do you solve the quadratic equation by completing the square: `x^2 – 8x + 12 = 0`?

Answer 1

Work out which factors of 12 add together to give 8. You can then factorise the equation. 12 is either `3*4` or `6*2` - `3+4 = 7` so that won't work, but `6 + 2 = 8` so that does work.

Explanation:

`(x - 6)(x-2) = 0`

Answer 2

`x=6` or `x=2`
`color(white)("XXXX")`(solved by completion of squares method)

Explanation:

Given `x^2–8x+12=0`

`color(white)("XXXX")`Move the constant to the right side
`x^2-8x = -12`
`color(white)("XXXX")`If `x^2` and `-8x` are the first two terms of a squared binomial:
`color(white)("XXXX")` `color(white)("XXXX")` `(x+a)^2 = x^2+2ax+a^2`
`color(white)("XXXX")`then the third term needs to be `(a^2) = (8/2)^2`
`x^2-8x+(8/2)^2 = -12 +(8/2)^2`

`x^2-8x+4^2 = -12 +16`

`color(white)("XXXX")`rewrite the left side as a squared binomial
`color(white)("XXXX")` and simplify the right side.
`(x-4)^2 = 4`

`color(white)("XXXX")`Take the square root of both sides
`x-4 = +-2`

`color(white)("XXXX")`Add 4 to both sides
`x=6`
or
`x=2`