Question

What are the solutions to the quadratic equation (5y + 6)2 = 24?b

Answer 1

Answer:

Step-by-step explanation:

Answer 2

ANSWER

The exact solution are:

$y = \frac{ - 6 - 2 \sqrt{6} }{5} \: \: or \: \: y = \frac{ - 6 + 2 \sqrt{6} }{5}$

EXPLANATION

The given quadratic equation is

${(5y + 6)}^{2} = 24$

We use the square root method to solve for y.

We take square root of both sides to get:

$\sqrt{{(5y + 6)}^{2}} = \pm\sqrt{24}$

This gives us:

$5y + 6 = \pm 2 \sqrt{6}$

Add -6 to both sides to get:

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

Divide through by 5:

$y = \frac{ - 6 \pm2 \sqrt{6} }{5}$

$y = \frac{ - 6 - 2 \sqrt{6} }{5} \: \: or \: \: y = \frac{ - 6 + 2 \sqrt{6} }{5}$