# How do you solve x- sqrt(3x + 7) = 7?

Aug 19, 2016

The soln. is $x = 14$, and, $x = 3$ is extraneous soln..

#### Explanation:

Rewriting the eqn. as, $x - 7 = \sqrt{3 x + 7}$, and, squaring, we get,

${x}^{2} - 14 x + 49 = 3 x + 7$.

$\Rightarrow {x}^{2} - 17 x + 42 = 0$.

Using, $14 \times 3 = 42 , \mathmr{and} , 14 + 3 = 17$, we have,

$\underline{{x}^{2} - 14 x} - \underline{3 x + 42} = 0$.

$\Rightarrow x \left(x - 14\right) - 3 \left(x - 14\right) = 0$.

$\Rightarrow \left(x - 14\right) \left(x - 3\right) = 0$.

$\Rightarrow x = 14 , \mathmr{and} , x = 3$.

Recall that $\sqrt{3 x + 7}$ is always $+ v e$, so that, $x = 3$ does not satisfy the original eqn., &, hence is an extraneous soln.

Thus, the soln. is $x = 14$, and, $x = 3$ is extraneous.