Question

what are the solutions to the quadratic equation $(5y + 6)^2 = 24$?

$\bigcirc$ $y = \frac{-6 + 2\sqrt{6}}{5}$ and $y = \frac{-6 - 2\sqrt{6}}{5}$

$\bigcirc$ $y = \frac{-6 + 2\sqrt{6}}{5}$ and $y = \frac{6 - 2\sqrt{6}}{5}$

$\bigcirc$ $y = \frac{-4\sqrt{6}}{5}$ and $y = \frac{-8\sqrt{6}}{5}$

$\bigcirc$ $y = \frac{4\sqrt{6}}{5}$ and $y = \frac{8\sqrt{6}}{5}$

Explanation:

Step1: Take square roots of both sides

$5y + 6 = \pm\sqrt{24} = \pm2\sqrt{6}$

Step2: Solve for y

$5y = -6 \pm 2\sqrt{6} \implies y = \frac{-6 \pm 2\sqrt{6}}{5}$

Answer:

A. $y=\frac{-6+2\sqrt{6}}{5}$ and $y=\frac{-6-2\sqrt{6}}{5}$