0=w^2+8w-90

Solution for 0=w^2+8w-90 equation:

Simplifying
0 = w2 + 8w + -90

Reorder the terms:
0 = -90 + 8w + w2

Solving
0 = -90 + 8w + w2

Solving for variable 'w'.

Combine like terms: 0 + 90 = 90
90 + -8w + -1w2 = -90 + 8w + w2 + 90 + -8w + -1w2

Reorder the terms:
90 + -8w + -1w2 = -90 + 90 + 8w + -8w + w2 + -1w2

Combine like terms: -90 + 90 = 0
90 + -8w + -1w2 = 0 + 8w + -8w + w2 + -1w2
90 + -8w + -1w2 = 8w + -8w + w2 + -1w2

Combine like terms: 8w + -8w = 0
90 + -8w + -1w2 = 0 + w2 + -1w2
90 + -8w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
90 + -8w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-90 + 8w + w2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 8w + 90 + w2 = 0 + 90

Reorder the terms:
-90 + 90 + 8w + w2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 8w + w2 = 0 + 90
8w + w2 = 0 + 90

Combine like terms: 0 + 90 = 90
8w + w2 = 90

The w term is 8w.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8w + 16 + w2 = 90 + 16

Reorder the terms:
16 + 8w + w2 = 90 + 16

Combine like terms: 90 + 16 = 106
16 + 8w + w2 = 106

Factor a perfect square on the left side:
(w + 4)(w + 4) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(w + 4) equal to 10.295630141 and -10.295630141.

Subproblem 1
w + 4 = 10.295630141

Simplifying
w + 4 = 10.295630141

Reorder the terms:
4 + w = 10.295630141

Solving
4 + w = 10.295630141

Solving for variable 'w'.

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

Add '-4' to each side of the equation.
4 + -4 + w = 10.295630141 + -4

Combine like terms: 4 + -4 = 0
0 + w = 10.295630141 + -4
w = 10.295630141 + -4

Combine like terms: 10.295630141 + -4 = 6.295630141
w = 6.295630141

Simplifying
w = 6.295630141

Subproblem 2
w + 4 = -10.295630141

Simplifying
w + 4 = -10.295630141

Reorder the terms:
4 + w = -10.295630141

Solving
4 + w = -10.295630141

Solving for variable 'w'.

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

Add '-4' to each side of the equation.
4 + -4 + w = -10.295630141 + -4

Combine like terms: 4 + -4 = 0
0 + w = -10.295630141 + -4
w = -10.295630141 + -4

Combine like terms: -10.295630141 + -4 = -14.295630141
w = -14.295630141

Simplifying
w = -14.295630141

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.295630141, -14.295630141}