# How do you solve sqrt(12x+13)=2x+1  and find any extraneous solutions?

May 6, 2018

color(indigo)("Extraneous solutions are : " x = 3, -1

#### Explanation:

$sqrt(12x + 13) = 2x + 1# $\text{Squaring both sides,} 12 x + 13 = {\left(2 x + 1\right)}^{2}$$12 x + 13 = 4 {x}^{2} + 4 x + 1$$4 {x}^{2} - 8 x - 12 = 0$$4 {x}^{2} + 4 x - 12 x - 12 = 0$$4 x \left(x + 1\right) - 12 \left(x + 1\right) = 0$$\left(4 x - 12\right) \cdot \left(x + 1\right) = 0$$x = \frac{12}{4} = 3 , - 1\$