# sqrt (4a + 29) = 2 sqrt (a) + 5? solve the equations.

Apr 18, 2017

#### Answer:

$a = \frac{1}{25}$

#### Explanation:

$\sqrt{4 a + 29} = 2 \sqrt{a} + 5$

Restrictions:
1. $4 a + 29 \ge 0$ or $a \ge - \frac{29}{4}$
2. $a \ge 0$

Combining the two restrictions for common segments, you get $a \ge 0$

${\left(\sqrt{4 a + 29}\right)}^{2} = {\left(2 \sqrt{a} + 5\right)}^{2}$
$4 a + 29 = 4 a + 20 \sqrt{a} + 25$
$20 \sqrt{a} = 4$
$\sqrt{a} = \frac{1}{5}$
${\left(\sqrt{a}\right)}^{2} = {\left(\frac{1}{5}\right)}^{2}$
$\therefore a = \frac{1}{25}$
This solution satisfies the restriction, thus is valid.