# How do you simplify 4- sqrt( r+6) = -sqrt( r-2)?

May 14, 2016

$r = 3$

#### Explanation:

grouping $4 = \sqrt{r + 6} - \sqrt{r - 2}$ and squaring both sides of the equation,
$16 = 4 + 2 r + 2 \sqrt{\left(r + 6\right) \left(r - 2\right)}$
Simplifying and grouping radicals to the right
$6 - r = \sqrt{\left(r + 6\right) \left(r - 2\right)}$
Squaring again both sides
(6-r)²=(r+6)(r-2)
After simplifications we get
$r = 3$