Question

How do you solve for `x` in `3(x-4)^2 - 6 = 40` ?

Answer 1

`x= 7.916 " or " 0.0842`

Explanation:

This is a specific form of a quadratic which does not have an `x` term. We can do this in a similar way to the method of completing the square, because the square is already there.

Isolate the bracket

`3(x-4)^2 - 6 = 40`

`3(x-4)^2 = 46`

`(x-4)^2 = 46/3" "` Find the square root of each side and solve .

`x-4 = +-sqrt(46/3)`

`x = sqrt(46/3) +4 " or " x = -sqrt(46/3)+4`

`x= 7.916 " or " 0.0842`

You could also multiply the whole expression out and then solve it as quadratic in the usual way with the formula.
This way is quicker..