# How do you solve -9(x-3)^2=-7?

Mar 13, 2018

$x = 3 \pm \frac{\sqrt{7}}{3}$

#### Explanation:

We need to solve for x. In order to isolate x, we first need to isolate the parenthesis:
${\left(x - 3\right)}^{2} = \frac{- 7}{-} 9 = \frac{7}{9}$
Next, we want to undo the squaring, so
$\left(x - 3\right) = \pm \sqrt{\frac{7}{9}}$
Then we can add the 3 to get x alone:
$x = 3 \pm \frac{\sqrt{7}}{3}$

Since it is a second degree equation, the two values (plus and minus) makes sense.