# How do you solve x= sqrt(3x+4) and find any extraneous solutions?

##### 1 Answer
Apr 17, 2017

We first conclude that $3 x + 4 \ge 0 \to x \ge - \frac{4}{3}$
The result of a radical may not be negative, so $x \ge 0$

#### Explanation:

Now we can square both sides:

$\to {x}^{2} = 3 x + 4$

Putting everything to one side we get:

$\to {x}^{2} - 3 x - 4 = 0$

Factoring:

$\to \left(x + 1\right) \left(x - 4\right) = 0 \to x = - 1 \mathmr{and} x = + 4$

After the initial conditions only $x = 4$ is left.