# How do you solve sqrt(2x-1) - sqrt(x+7) = 0?

Jan 24, 2016

$x = 8$

#### Explanation:

$\sqrt{2 x - 1} - \sqrt{x + 7} = 0$

$\implies \sqrt{2 x - 1} = \sqrt{x + 7}$

$\implies 2 x - 1 = x + 7$

$\implies 2 x - x = 7 + 1$

$\implies x = 8$

Feb 21, 2016

$x = 8$

#### Explanation:

color(blue)(sqrt(2x-1)-sqrt(x+7)=0

Add $\sqrt{x + 7}$ both sides

$\rightarrow \sqrt{2 x - 1} = \sqrt{x + 7}$

Square both sides to get rid of the radical sign

$\rightarrow {\left(\sqrt{2 x - 1}\right)}^{2} = {\left(\sqrt{x + 7}\right)}^{2}$

$\rightarrow 2 x - 1 = x + 7$

Subtract $x$ both sides

$\rightarrow x - 1 = 7$

color(green)(rArrx=7+1=8

Check

color(brown)(sqrt(2(8)-1)-sqrt(8+7)=0

color(brown)(sqrt(16-1)-sqrt(8+7)=0

color(brown)(sqrt15-sqrt15=0

So,It is true