(w-2)(w)=112

Solution for (w-2)(w)=112 equation:

Simplifying
(w + -2)(w) = 112

Reorder the terms:
(-2 + w)(w) = 112

Reorder the terms for easier multiplication:
w(-2 + w) = 112
(-2 * w + w * w) = 112
(-2w + w2) = 112

Solving
-2w + w2 = 112

Solving for variable 'w'.

Reorder the terms:
-112 + -2w + w2 = 112 + -112

Combine like terms: 112 + -112 = 0
-112 + -2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '112' to each side of the equation.
-112 + -2w + 112 + w2 = 0 + 112

Reorder the terms:
-112 + 112 + -2w + w2 = 0 + 112

Combine like terms: -112 + 112 = 0
0 + -2w + w2 = 0 + 112
-2w + w2 = 0 + 112

Combine like terms: 0 + 112 = 112
-2w + w2 = 112

The w term is -2w.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2w + 1 + w2 = 112 + 1

Reorder the terms:
1 + -2w + w2 = 112 + 1

Combine like terms: 112 + 1 = 113
1 + -2w + w2 = 113

Factor a perfect square on the left side:
(w + -1)(w + -1) = 113

Calculate the square root of the right side: 10.630145813

Break this problem into two subproblems by setting 
(w + -1) equal to 10.630145813 and -10.630145813.

Subproblem 1
w + -1 = 10.630145813

Simplifying
w + -1 = 10.630145813

Reorder the terms:
-1 + w = 10.630145813

Solving
-1 + w = 10.630145813

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = 10.630145813 + 1

Combine like terms: -1 + 1 = 0
0 + w = 10.630145813 + 1
w = 10.630145813 + 1

Combine like terms: 10.630145813 + 1 = 11.630145813
w = 11.630145813

Simplifying
w = 11.630145813

Subproblem 2
w + -1 = -10.630145813

Simplifying
w + -1 = -10.630145813

Reorder the terms:
-1 + w = -10.630145813

Solving
-1 + w = -10.630145813

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = -10.630145813 + 1

Combine like terms: -1 + 1 = 0
0 + w = -10.630145813 + 1
w = -10.630145813 + 1

Combine like terms: -10.630145813 + 1 = -9.630145813
w = -9.630145813

Simplifying
w = -9.630145813

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {11.630145813, -9.630145813}