Question

How do you solve using the completing the square method `x^2- 8x + 12 = 0`?

Answer 1

`x=2" or "x=6`

Explanation:

`"place the constant term on the right side"`

`rArrx^2-8x=-12`

`"to use the method of "color(blue)"completing the square"`

`• " ensure the coefficient of the "x^2" term is 1"`

`x^2-8x=-12larrcolor(blue)"coefficient of 1"`

`• " add "(1/2"coefficient of x-term")^2" to both sides"`

`x^2+2(-4)xcolor(red)(+16)=-12color(red)(+16)`

`rArr(x-4)^2=4`

`color(blue)"take the square root of both sides"`

`rArrx-4=+-sqrt4larrcolor(blue)"note plus or minus"`

`rArrx=4+-2`

`rArrx=4+2=6" or "x=4-2=2`