Question

Helppppp pls simple algebra hella points show your work

Answer 1

`\Huge \boxed{y=-7 \ \ \mathrm{or} \ \ y=-3}`

`\rule[225]{225}{2}`

Explanation:

`(y-3)^2 =2y^2 +4y+30`

Expanding brackets.

`y^2-6y+9=2y^2 +4y+30`

Subtracting (y² - 6y + 9) from both sides, then switching sides.

`y^2 +10y+21=0`

Factoring left side.

`(y+3)(y+7)=0`

Setting factors equal to 0.

`\Longrightarrow y+3= 0 \\\\\\ \Longrightarrow y=-3`

`\Longrightarrow y+7=0 \\\\\\ \Longrightarrow y=-7`

`\rule[225]{225}{2}`

Answer 2

y = -7, y = -3

Explanation:

(y - 3)² = 2y² + 4y + 30

expand:

y² - 6y + 9 = 2y² + 4y + 30

subtract 30 from both sides

y² - 6y + 9 - 30= 2y² + 4y + 30 - 30

simplify:

y² - 6y - 21 = 2y² + 4y

subtract 4y from both sides

y² - 6y - 21 -4y = 2y² + 4y - 4y

simplify:

y² - 10y - 21 = 2y²

subtract 2y² from both sides

y² - 10y - 21 - 2y² = 2y² - 2y²

simplify:

-y² - 10y - 21 = 0

solve y by quadratic equation

- (-10) ± √ (-10² - 4(-1)(21)

y = --------------------------------------

2(-1)

y = -7, y = -3