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

Feb 18, 2016

$x = 9 \mathmr{and} x = \frac{1}{9}$

Explanation:

Squaring both sides we get $\left(x + 7\right) - 2 \cdot \sqrt{x + 7} \cdot 2 \sqrt{x} + 4 \cdot x = 4$
or $5 \cdot x + 3 = 4 \cdot \sqrt{x \left(x + 7\right)}$ Squaring both sides we get ${\left(5 \cdot x + 3\right)}^{2} = 16 \cdot x \cdot \left(x + 7\right)$or $25 \cdot {x}^{2} + 30 \cdot x + 9 = 16 \cdot {x}^{2} + 112 \cdot x$ or
$9 \cdot {x}^{2} - 82 \cdot x + 9 = 0$ or $\left(x - 9\right) \left(9 x - 1\right) = 0$ or $x = 9 \mathmr{and} x = \frac{1}{9}$[answer]