# How do you solve sqrt(2x+2) - sqrt(x+2) = 1?

Nov 2, 2015

X = 7

#### Explanation:

Start off by shifting;
$\sqrt{2 x + 2} = \sqrt{x + 2} + 1$

Square both sides;

$2 x + 2 = \left(x + 2\right) + 1 + 2 \sqrt{x + 2}$

Simplify as much as possible;

$x - 1 = 2 \sqrt{x + 2}$

Square once again;

${x}^{2} + 1 - 2 x = 4 \left(x + 2\right)$

${x}^{2} + 1 - 2 x = 4 x + 8$
Simplify;
${x}^{2} - 6 x - 7 = 0$

Factor;

$\left(x - 7\right) \left(x + 1\right) = 0$

So $x = 7 \mathmr{and} - 1$

But now we can be hasty in saying it has 2 solutions;

# Make sute both solutions are real

Lets check for 7

$\sqrt{2 x + 2} - \sqrt{x + 2}$

Lets check for -1

# $\therefore$ -1 is not a solution

We end up with x = 7