4y^2+34y=-144

Solution for 4y^2+34y=-144 equation:

Simplifying
4y2 + 34y = -144

Reorder the terms:
34y + 4y2 = -144

Solving
34y + 4y2 = -144

Solving for variable 'y'.

Reorder the terms:
144 + 34y + 4y2 = -144 + 144

Combine like terms: -144 + 144 = 0
144 + 34y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(72 + 17y + 2y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(72 + 17y + 2y2)' equal to zero and attempt to solve:

Simplifying
72 + 17y + 2y2 = 0

Solving
72 + 17y + 2y2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
36 + 8.5y + y2 = 0

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 8.5y + -36 + y2 = 0 + -36

Reorder the terms:
36 + -36 + 8.5y + y2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 8.5y + y2 = 0 + -36
8.5y + y2 = 0 + -36

Combine like terms: 0 + -36 = -36
8.5y + y2 = -36

The y term is 8.5y.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5y + 18.0625 + y2 = -36 + 18.0625

Reorder the terms:
18.0625 + 8.5y + y2 = -36 + 18.0625

Combine like terms: -36 + 18.0625 = -17.9375
18.0625 + 8.5y + y2 = -17.9375

Factor a perfect square on the left side:
(y + 4.25)(y + 4.25) = -17.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.