# How do you solve sqrt( 2x - 2 ) + sqrt( 7x + 4 ) = sqrt( 13x + 10)?

Jun 22, 2018

$x = 3$

#### Explanation:

Squaring the given equation

$2 x - 2 + 7 x + 4 + 2 \sqrt{2 x - 2} \sqrt{7 x + 4} = 13 x + 10$

$\sqrt{2 x - 2} \sqrt{7 x + 4} = 2 x + 4$

squaring again and simplifying we get

${x}^{2} - \frac{11}{5} x - \frac{12}{5} = 0$
solving this equation we get

${x}_{1} = 3$
${x}_{2} = - \frac{4}{5}$ which is not a solution!