w(w+5)=100

Solution for w(w+5)=100 equation:

Simplifying
w(w + 5) = 100

Reorder the terms:
w(5 + w) = 100
(5 * w + w * w) = 100
(5w + w2) = 100

Solving
5w + w2 = 100

Solving for variable 'w'.

Reorder the terms:
-100 + 5w + w2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 5w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 5w + 100 + w2 = 0 + 100

Reorder the terms:
-100 + 100 + 5w + w2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 5w + w2 = 0 + 100
5w + w2 = 0 + 100

Combine like terms: 0 + 100 = 100
5w + w2 = 100

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = 100 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 100 + 6.25

Combine like terms: 100 + 6.25 = 106.25
6.25 + 5w + w2 = 106.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(w + 2.5) equal to 10.307764064 and -10.307764064.

Subproblem 1
w + 2.5 = 10.307764064

Simplifying
w + 2.5 = 10.307764064

Reorder the terms:
2.5 + w = 10.307764064

Solving
2.5 + w = 10.307764064

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = 10.307764064 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 10.307764064 + -2.5
w = 10.307764064 + -2.5

Combine like terms: 10.307764064 + -2.5 = 7.807764064
w = 7.807764064

Simplifying
w = 7.807764064

Subproblem 2
w + 2.5 = -10.307764064

Simplifying
w + 2.5 = -10.307764064

Reorder the terms:
2.5 + w = -10.307764064

Solving
2.5 + w = -10.307764064

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = -10.307764064 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -10.307764064 + -2.5
w = -10.307764064 + -2.5

Combine like terms: -10.307764064 + -2.5 = -12.807764064
w = -12.807764064

Simplifying
w = -12.807764064

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.807764064, -12.807764064}