CPM Homework Help : A2C Problem 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?

Hint:

Square both sides of the equation.

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

Hint 2:

Simplify and solve the resulting equation.

$x^{2} − 2x − 3 = 0$

Answer:

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

Checking:

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

$6=\sqrt{36}$

$6 = 6$

$-2=\sqrt{4}$

$−2 = 2$