88=(w+1)w

Solution for 88=(w+1)w equation:

Simplifying
88 = (w + 1) * w

Reorder the terms:
88 = (1 + w) * w

Reorder the terms for easier multiplication:
88 = w(1 + w)
88 = (1 * w + w * w)
88 = (1w + w2)

Solving
88 = 1w + w2

Solving for variable 'w'.

Reorder the terms:
88 + -1w + -1w2 = 1w + -1w + w2 + -1w2

Combine like terms: 1w + -1w = 0
88 + -1w + -1w2 = 0 + w2 + -1w2
88 + -1w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
88 + -1w + -1w2 = 0

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

Divide each side by '-1'.
-88 + w + w2 = 0

Move the constant term to the right:

Add '88' to each side of the equation.
-88 + w + 88 + w2 = 0 + 88

Reorder the terms:
-88 + 88 + w + w2 = 0 + 88

Combine like terms: -88 + 88 = 0
0 + w + w2 = 0 + 88
w + w2 = 0 + 88

Combine like terms: 0 + 88 = 88
w + w2 = 88

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + w2 = 88 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + w2 = 88 + 0.25

Combine like terms: 88 + 0.25 = 88.25
1.25 + w2 = 88.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 88.25

Calculate the square root of the right side: 9.394147114

Break this problem into two subproblems by setting 
(w + 0.5) equal to 9.394147114 and -9.394147114.

Subproblem 1
w + 0.5 = 9.394147114

Simplifying
w + 0.5 = 9.394147114

Reorder the terms:
0.5 + w = 9.394147114

Solving
0.5 + w = 9.394147114

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = 9.394147114 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 9.394147114 + -0.5
w = 9.394147114 + -0.5

Combine like terms: 9.394147114 + -0.5 = 8.894147114
w = 8.894147114

Simplifying
w = 8.894147114

Subproblem 2
w + 0.5 = -9.394147114

Simplifying
w + 0.5 = -9.394147114

Reorder the terms:
0.5 + w = -9.394147114

Solving
0.5 + w = -9.394147114

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = -9.394147114 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -9.394147114 + -0.5
w = -9.394147114 + -0.5

Combine like terms: -9.394147114 + -0.5 = -9.894147114
w = -9.894147114

Simplifying
w = -9.894147114

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.894147114, -9.894147114}