2y^2+8y-32=0

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Solution for 2y^2+8y-32=0 equation: 


Simplifying
2y2 + 8y + -32 = 0

Reorder the terms:
-32 + 8y + 2y2 = 0

Solving
-32 + 8y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 4y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + 4y + y2)' equal to zero and attempt to solve:

Simplifying
-16 + 4y + y2 = 0

Solving
-16 + 4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 4y + 16 + y2 = 0 + 16

Reorder the terms:
-16 + 16 + 4y + y2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 4y + y2 = 0 + 16
4y + y2 = 0 + 16

Combine like terms: 0 + 16 = 16
4y + y2 = 16

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 16 + 4

Reorder the terms:
4 + 4y + y2 = 16 + 4

Combine like terms: 16 + 4 = 20
4 + 4y + y2 = 20

Factor a perfect square on the left side:
(y + 2)(y + 2) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(y + 2) equal to 4.472135955 and -4.472135955.


Subproblem 1
y + 2 = 4.472135955

Simplifying
y + 2 = 4.472135955

Reorder the terms:
2 + y = 4.472135955

Solving
2 + y = 4.472135955

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + y = 4.472135955 + -2

Combine like terms: 2 + -2 = 0
0 + y = 4.472135955 + -2
y = 4.472135955 + -2

Combine like terms: 4.472135955 + -2 = 2.472135955
y = 2.472135955

Simplifying
y = 2.472135955


Subproblem 2
y + 2 = -4.472135955

Simplifying
y + 2 = -4.472135955

Reorder the terms:
2 + y = -4.472135955

Solving
2 + y = -4.472135955

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + y = -4.472135955 + -2

Combine like terms: 2 + -2 = 0
0 + y = -4.472135955 + -2
y = -4.472135955 + -2

Combine like terms: -4.472135955 + -2 = -6.472135955
y = -6.472135955

Simplifying
y = -6.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.472135955, -6.472135955}
Solution
y = {2.472135955, -6.472135955}

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