w^2+13w-64=100

Solution for w^2+13w-64=100 equation:

Simplifying
w2 + 13w + -64 = 100

Reorder the terms:
-64 + 13w + w2 = 100

Solving
-64 + 13w + w2 = 100

Solving for variable 'w'.

Reorder the terms:
-64 + -100 + 13w + w2 = 100 + -100

Combine like terms: -64 + -100 = -164
-164 + 13w + w2 = 100 + -100

Combine like terms: 100 + -100 = 0
-164 + 13w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '164' to each side of the equation.
-164 + 13w + 164 + w2 = 0 + 164

Reorder the terms:
-164 + 164 + 13w + w2 = 0 + 164

Combine like terms: -164 + 164 = 0
0 + 13w + w2 = 0 + 164
13w + w2 = 0 + 164

Combine like terms: 0 + 164 = 164
13w + w2 = 164

The w term is 13w.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13w + 42.25 + w2 = 164 + 42.25

Reorder the terms:
42.25 + 13w + w2 = 164 + 42.25

Combine like terms: 164 + 42.25 = 206.25
42.25 + 13w + w2 = 206.25

Factor a perfect square on the left side:
(w + 6.5)(w + 6.5) = 206.25

Calculate the square root of the right side: 14.361406616

Break this problem into two subproblems by setting 
(w + 6.5) equal to 14.361406616 and -14.361406616.

Subproblem 1
w + 6.5 = 14.361406616

Simplifying
w + 6.5 = 14.361406616

Reorder the terms:
6.5 + w = 14.361406616

Solving
6.5 + w = 14.361406616

Solving for variable 'w'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + w = 14.361406616 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + w = 14.361406616 + -6.5
w = 14.361406616 + -6.5

Combine like terms: 14.361406616 + -6.5 = 7.861406616
w = 7.861406616

Simplifying
w = 7.861406616

Subproblem 2
w + 6.5 = -14.361406616

Simplifying
w + 6.5 = -14.361406616

Reorder the terms:
6.5 + w = -14.361406616

Solving
6.5 + w = -14.361406616

Solving for variable 'w'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + w = -14.361406616 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + w = -14.361406616 + -6.5
w = -14.361406616 + -6.5

Combine like terms: -14.361406616 + -6.5 = -20.861406616
w = -20.861406616

Simplifying
w = -20.861406616

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.861406616, -20.861406616}