w^2+19w-88=0

Solution for w^2+19w-88=0 equation:

Simplifying
w2 + 19w + -88 = 0

Reorder the terms:
-88 + 19w + w2 = 0

Solving
-88 + 19w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '88' to each side of the equation.
-88 + 19w + 88 + w2 = 0 + 88

Reorder the terms:
-88 + 88 + 19w + w2 = 0 + 88

Combine like terms: -88 + 88 = 0
0 + 19w + w2 = 0 + 88
19w + w2 = 0 + 88

Combine like terms: 0 + 88 = 88
19w + w2 = 88

The w term is 19w.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19w + 90.25 + w2 = 88 + 90.25

Reorder the terms:
90.25 + 19w + w2 = 88 + 90.25

Combine like terms: 88 + 90.25 = 178.25
90.25 + 19w + w2 = 178.25

Factor a perfect square on the left side:
(w + 9.5)(w + 9.5) = 178.25

Calculate the square root of the right side: 13.351029923

Break this problem into two subproblems by setting 
(w + 9.5) equal to 13.351029923 and -13.351029923.

Subproblem 1
w + 9.5 = 13.351029923

Simplifying
w + 9.5 = 13.351029923

Reorder the terms:
9.5 + w = 13.351029923

Solving
9.5 + w = 13.351029923

Solving for variable 'w'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + w = 13.351029923 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + w = 13.351029923 + -9.5
w = 13.351029923 + -9.5

Combine like terms: 13.351029923 + -9.5 = 3.851029923
w = 3.851029923

Simplifying
w = 3.851029923

Subproblem 2
w + 9.5 = -13.351029923

Simplifying
w + 9.5 = -13.351029923

Reorder the terms:
9.5 + w = -13.351029923

Solving
9.5 + w = -13.351029923

Solving for variable 'w'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + w = -13.351029923 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + w = -13.351029923 + -9.5
w = -13.351029923 + -9.5

Combine like terms: -13.351029923 + -9.5 = -22.851029923
w = -22.851029923

Simplifying
w = -22.851029923

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.851029923, -22.851029923}