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

Jun 15, 2016

Start by squaring both sides.

#### Explanation:

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

$2 x - 1 = {x}^{2} - 4 x + 4$

$0 = {x}^{2} - 6 x + 5$

$0 = \left(x - 5\right) \left(x - 1\right)$

$x = 5 \mathmr{and} 1$

Checking in the original equation, we find that only $x = 5$ works. Our solution set is therefore $\left\{x = 5\right\}$.

Hopefully this helps!