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

Jul 20, 2016

$x = 7.916 \text{ or } 0.0842$

#### 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

$3 {\left(x - 4\right)}^{2} - 6 = 40$

$3 {\left(x - 4\right)}^{2} = 46$

${\left(x - 4\right)}^{2} = \frac{46}{3} \text{ }$ Find the square root of each side and solve .

$x - 4 = \pm \sqrt{\frac{46}{3}}$

$x = \sqrt{\frac{46}{3}} + 4 \text{ or } x = - \sqrt{\frac{46}{3}} + 4$

$x = 7.916 \text{ or } 0.0842$

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..