How do you solve sqrt( x + 7) = 2 sqrtx?

Jun 29, 2017

Get rid of the square roots.

${\left(\sqrt{x + 7}\right)}^{2} = {\left(2 \sqrt{x}\right)}^{2}$

$x + 7 = 4 x$

$3 x = 7$

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

Jun 29, 2017

The answer is $\frac{7}{3}$.

Explanation:

$\sqrt{x + 7}$ = 2$\sqrt{x}$

${\left(\sqrt{x + 7}\right)}^{2}$ = ${\left(2 \sqrt{x}\right)}^{2}$

$x + 7$ = $4 x$

$7$ = $4 x - x$

$7 = 3 x$

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