2w^2+8w-180=0

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Solution for 2w^2+8w-180=0 equation: 


Simplifying
2w2 + 8w + -180 = 0

Reorder the terms:
-180 + 8w + 2w2 = 0

Solving
-180 + 8w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 4w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + 4w + w2)' equal to zero and attempt to solve:

Simplifying
-90 + 4w + w2 = 0

Solving
-90 + 4w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 4w + 90 + w2 = 0 + 90

Reorder the terms:
-90 + 90 + 4w + w2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 4w + w2 = 0 + 90
4w + w2 = 0 + 90

Combine like terms: 0 + 90 = 90
4w + w2 = 90

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

Add '4' to each side of the equation.
4w + 4 + w2 = 90 + 4

Reorder the terms:
4 + 4w + w2 = 90 + 4

Combine like terms: 90 + 4 = 94
4 + 4w + w2 = 94

Factor a perfect square on the left side:
(w + 2)(w + 2) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(w + 2) equal to 9.695359715 and -9.695359715.


Subproblem 1
w + 2 = 9.695359715

Simplifying
w + 2 = 9.695359715

Reorder the terms:
2 + w = 9.695359715

Solving
2 + w = 9.695359715

Solving for variable 'w'.

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

Add '-2' to each side of the equation.
2 + -2 + w = 9.695359715 + -2

Combine like terms: 2 + -2 = 0
0 + w = 9.695359715 + -2
w = 9.695359715 + -2

Combine like terms: 9.695359715 + -2 = 7.695359715
w = 7.695359715

Simplifying
w = 7.695359715


Subproblem 2
w + 2 = -9.695359715

Simplifying
w + 2 = -9.695359715

Reorder the terms:
2 + w = -9.695359715

Solving
2 + w = -9.695359715

Solving for variable 'w'.

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

Add '-2' to each side of the equation.
2 + -2 + w = -9.695359715 + -2

Combine like terms: 2 + -2 = 0
0 + w = -9.695359715 + -2
w = -9.695359715 + -2

Combine like terms: -9.695359715 + -2 = -11.695359715
w = -11.695359715

Simplifying
w = -11.695359715


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.695359715, -11.695359715}
Solution
w = {7.695359715, -11.695359715}

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