(w+5)(w)=112

Solution for (w+5)(w)=112 equation:

Simplifying
(w + 5)(w) = 112

Reorder the terms:
(5 + w)(w) = 112

Reorder the terms for easier multiplication:
w(5 + w) = 112
(5 * w + w * w) = 112
(5w + w2) = 112

Solving
5w + w2 = 112

Solving for variable 'w'.

Reorder the terms:
-112 + 5w + w2 = 112 + -112

Combine like terms: 112 + -112 = 0
-112 + 5w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '112' to each side of the equation.
-112 + 5w + 112 + w2 = 0 + 112

Reorder the terms:
-112 + 112 + 5w + w2 = 0 + 112

Combine like terms: -112 + 112 = 0
0 + 5w + w2 = 0 + 112
5w + w2 = 0 + 112

Combine like terms: 0 + 112 = 112
5w + w2 = 112

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 = 112 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 112 + 6.25

Combine like terms: 112 + 6.25 = 118.25
6.25 + 5w + w2 = 118.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 118.25

Calculate the square root of the right side: 10.874281585

Break this problem into two subproblems by setting 
(w + 2.5) equal to 10.874281585 and -10.874281585.

Subproblem 1
w + 2.5 = 10.874281585

Simplifying
w + 2.5 = 10.874281585

Reorder the terms:
2.5 + w = 10.874281585

Solving
2.5 + w = 10.874281585

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 = 10.874281585 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 10.874281585 + -2.5
w = 10.874281585 + -2.5

Combine like terms: 10.874281585 + -2.5 = 8.374281585
w = 8.374281585

Simplifying
w = 8.374281585

Subproblem 2
w + 2.5 = -10.874281585

Simplifying
w + 2.5 = -10.874281585

Reorder the terms:
2.5 + w = -10.874281585

Solving
2.5 + w = -10.874281585

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 = -10.874281585 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -10.874281585 + -2.5
w = -10.874281585 + -2.5

Combine like terms: -10.874281585 + -2.5 = -13.374281585
w = -13.374281585

Simplifying
w = -13.374281585

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.374281585, -13.374281585}