W(W+23)=698

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Solution for W(W+23)=698 equation: 


Simplifying
W(W + 23) = 698

Reorder the terms:
W(23 + W) = 698
(23 * W + W * W) = 698
(23W + W2) = 698

Solving
23W + W2 = 698

Solving for variable 'W'.

Reorder the terms:
-698 + 23W + W2 = 698 + -698

Combine like terms: 698 + -698 = 0
-698 + 23W + W2 = 0

Begin completing the square.

Move the constant term to the right:

Add '698' to each side of the equation.
-698 + 23W + 698 + W2 = 0 + 698

Reorder the terms:
-698 + 698 + 23W + W2 = 0 + 698

Combine like terms: -698 + 698 = 0
0 + 23W + W2 = 0 + 698
23W + W2 = 0 + 698

Combine like terms: 0 + 698 = 698
23W + W2 = 698

The W term is 23W.  Take half its coefficient (11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
23W + 132.25 + W2 = 698 + 132.25

Reorder the terms:
132.25 + 23W + W2 = 698 + 132.25

Combine like terms: 698 + 132.25 = 830.25
132.25 + 23W + W2 = 830.25

Factor a perfect square on the left side:
(W + 11.5)(W + 11.5) = 830.25

Calculate the square root of the right side: 28.814059068

Break this problem into two subproblems by setting 
(W + 11.5) equal to 28.814059068 and -28.814059068.


Subproblem 1
W + 11.5 = 28.814059068

Simplifying
W + 11.5 = 28.814059068

Reorder the terms:
11.5 + W = 28.814059068

Solving
11.5 + W = 28.814059068

Solving for variable 'W'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + W = 28.814059068 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + W = 28.814059068 + -11.5
W = 28.814059068 + -11.5

Combine like terms: 28.814059068 + -11.5 = 17.314059068
W = 17.314059068

Simplifying
W = 17.314059068


Subproblem 2
W + 11.5 = -28.814059068

Simplifying
W + 11.5 = -28.814059068

Reorder the terms:
11.5 + W = -28.814059068

Solving
11.5 + W = -28.814059068

Solving for variable 'W'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + W = -28.814059068 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + W = -28.814059068 + -11.5
W = -28.814059068 + -11.5

Combine like terms: -28.814059068 + -11.5 = -40.314059068
W = -40.314059068

Simplifying
W = -40.314059068


Solution
The solution to the problem is based on the solutions
from the subproblems.
W = {17.314059068, -40.314059068}

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