Question

How do you solve `x^2-24x=10` by completing the square?

Answer 1

`x = 24.4097, -0.4097`

Explanation:

`x^2 -24x = 10`

`x^2 + (2 (x) (-12) ) = 10`

`x^2 + ( 2 (x) (-12) ) +144 -144 = 10` (Add and subtract 144)#

`x^2 + ( 2 (x)(-12) + (12)^2 = 154`
`(x-12)^2 = 154`
`(x-12) = +-sqrt 154 color (white)(aaa)`taking square root on both sides
`x = 12 +- sqrt154`
`x = 24.4097, -0.4097`

Answer 2

`x=12+-sqrt(154)`

Explanation:

Completing the square means making the `x^2` and `x` terms take the form `x^2 +2nx +n^2`. Where in this case `n=-12`.

So, `x^2-24x=10` becomes `x^2 -24x+144=10+144`.
So, `(x-12)^2=154`
`x=12+-sqrt(154)`