Solve and check the equation for y.

Question

2y^2+9y+35=(y+7)^2.

Answer 1

2y^2 + 9y + 35 = (y + 7)^2

2y^2 + 9y + 35 = y^2 + 49 + 14y

Bring all the terms to left side.

2y^2 + 9y + 35 - y^2 - 49 -14y = 0

y^2 - 5y  - 14 = 0

y^2 - 7y + 2y -14 = 0

y(y - 7) + 2(y - 7) = 0

Take common out (y - 7).

(y - 7)(y + 2) = 0

y - 7 = 0

Add 7 to each side.

y = 7.

And y + 2 = 0

Subtract 2 from each side.

y = -2.

Solution y  = -2 and 7.

Check :

Substitute the value of y = - 2 in the original equation.

2(-2)^2 + 9(-2) + 35 ≟ ((-2) + 7)^2

8 - 18 + 35 ≟ 25

25 = 25.

The above statement is true, so the value of y = - 2 is the solution of the original inequality.

Substitute the value of y = 7 in the original equation.

2(7)^2 + 9(7) + 35 ≟ (7 + 7)^2

98 + 63 + 35 ≟ 196

196 = 196.

The above statement is true, so the value of y = 7 is the solution of the original inequality.