Question

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

Answer 1

`x= 6+sqrt(38)` or `x=6-sqrt(38)`
`color(white)("XXXX")`(using the completing the squares method)

Explanation:

Given `x^2-12x-2 = 0`

Completing the square is simpler if we move the constant to the right side:
`color(white)("XXXX")` `x^2-12x = 2`

If `x^2` and `-12x` are the first two terms of a squared binomial expansion:
`color(white)("XXXX")` `(x-a)^2 = (x^2-2ax+a^2)`
then
`color(white)("XXXX")` `a=6`
and
we need to add `a^2 = 36` to both sides to complete the square

`color(white)("XXXX")` `x^2-12x+36 = 2+36`

Rewriting as a squared binomial (and simplifying the right side)
`color(white)("XXXX")` `(x-6)^2 = 38`

Taking the square root of both sides
`color(white)("XXXX")` `x-6 = +-sqrt(38)`

Adding `6` to both sides:
`color(white)("XXXX")` `x=6+-sqrt(38)`