Question

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

Answer 1

The exact solution are:

`y = ( - 6 - 2 √(6) )/(5) \: \: or \: \: y = ( - 6 + 2 √(6) )/(5)`

Step-by-step 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√(24)`

This gives us:

`5y + 6 = \pm 2 √(6)`

Add -6 to both sides to get:

`5y = - 6 \pm 2 √(6)`

Divide through by 5:

`y = ( - 6 \pm2 √(6) )/(5)`

`y = ( - 6 - 2 √(6) )/(5) \: \: or \: \: y = ( - 6 + 2 √(6) )/(5)`