# How do you simplify sqrt( 14-a) =sqrt( a+3) +3?

Apr 5, 2017

I have taken you step by step to a point where you may take over.
A lot of detail is given.

#### Explanation:

Square both sides

$14 - a = \left(a + 3\right) + 6 \sqrt{a + 3} + 9$

Subtract $\left(a + 3\right)$ from both sides

$11 - 2 a = 6 \sqrt{a + 3} + 9$

Subtract 9 from both sides

$2 - 2 a = 6 \sqrt{a + 3}$

Divide both sides by 6

$\frac{1}{3} - \frac{a}{3} = \sqrt{a + 3}$

Square both sides

$\frac{1}{9} - \frac{2}{3} \left(\frac{a}{3}\right) + {a}^{2} / 9 = a + 3$

$- \frac{26}{9} - \frac{2 a}{9} - \frac{9 a}{9} + {a}^{2} / 9 = 0$

$- \frac{26}{9} - \frac{11 a}{9} + {a}^{2} / 9 = 0$

$- 26 - 11 a + {a}^{2} = 0$