# How do you solve sqrt(x+2)-7=sqrt(x+9?

Apr 23, 2017

No solutions exist.

#### Explanation:

$\sqrt{x + 2} - 7 = \sqrt{x + 9}$. Squaring both sides , we get

$\left(\cancel{x} + 2\right) - 2 \cdot 7 \cdot \sqrt{x + 2} + 49 = \left(\cancel{x} + 9\right)$ or

$2 - 14 \sqrt{x + 2} + 49 = 9 \mathmr{and} 14 \sqrt{x + 2} = 42 \mathmr{and} \sqrt{x + 2} = 3$

Squaring both sides , we get $x + 2 = 9 \mathmr{and} x = 7$ [Ans]

Check:

$\sqrt{7 + 2} - 7 = \sqrt{7 + 9}$

$\sqrt{9} - 7 = \sqrt{16}$

$3 - 7 = 4$

$- 4 = 4$

No solutions exist.

I entered the equation into a computation engine named, WolframAlpha ; it returned that no solutions exist.