### Home > A2C > Chapter 3 > Lesson 3.2.3 > Problem3-129

3-129.

Solve $2 x = \sqrt { 8 x + 12 }$ by first rewriting the equation as an equivalent equation without the square-root sign. After solving the new equation, answer these questions: Do both answers make the original equation true? Was the equation that led to the two solutions equivalent to the original equation? Why or why not?

Square both sides of the equation.

$4x^{2} = 8x + 12$

Simplify and solve the resulting equation.

$x^{2} − 2x − 3 = 0$

$x = 3$. But, $−1$ does not work in the original equation.

Substitute each answer in the original equation. Only one of them will satisfy the equation.

$6=\sqrt{36}$

$6 = 6$

$-2=\sqrt{4}$

$−2 = 2$