How do you solve (4x + 3)^2 = 6?

Sep 29, 2016

Take the square root then solve two linear equations.

Explanation:

Since we have a squared term, lets begin by taking the square root of both sides, so that we have:

$4 x + 3 = \pm \sqrt{6}$

Let's subtract 3 on both sides:

$4 x = \pm \sqrt{6} - 3$

Then divide by 4:

$x = \frac{\pm \sqrt{6} - 3}{4}$

So we have two solutions:

$x = \frac{\sqrt{6} - 3}{4}$

$x = \frac{- \sqrt{6} - 3}{4}$

Including the $\pm$ is important, or else we would have missed one of the solutions.