100=w^2+w

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Solution for 100=w^2+w equation:


Simplifying
100 = w2 + w

Reorder the terms:
100 = w + w2

Solving
100 = w + w2

Solving for variable 'w'.

Reorder the terms:
100 + -1w + -1w2 = w + -1w + w2 + -1w2

Combine like terms: w + -1w = 0
100 + -1w + -1w2 = 0 + w2 + -1w2
100 + -1w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
100 + -1w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-100 + w + w2 = 0

Move the constant term to the right:

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

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

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

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

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + w2 = 100 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + w2 = 100 + 0.25

Combine like terms: 100 + 0.25 = 100.25
1.25 + w2 = 100.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(w + 0.5) equal to 10.012492197 and -10.012492197.

Subproblem 1

w + 0.5 = 10.012492197 Simplifying w + 0.5 = 10.012492197 Reorder the terms: 0.5 + w = 10.012492197 Solving 0.5 + w = 10.012492197 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 10.012492197 + -0.5 w = 10.012492197 + -0.5 Combine like terms: 10.012492197 + -0.5 = 9.512492197 w = 9.512492197 Simplifying w = 9.512492197

Subproblem 2

w + 0.5 = -10.012492197 Simplifying w + 0.5 = -10.012492197 Reorder the terms: 0.5 + w = -10.012492197 Solving 0.5 + w = -10.012492197 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -10.012492197 + -0.5 w = -10.012492197 + -0.5 Combine like terms: -10.012492197 + -0.5 = -10.512492197 w = -10.512492197 Simplifying w = -10.512492197

Solution

The solution to the problem is based on the solutions from the subproblems. w = {9.512492197, -10.512492197}

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