8-4w=13+w^2

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Solution for 8-4w=13+w^2 equation: 


Simplifying
8 + -4w = 13 + w2

Solving
8 + -4w = 13 + w2

Solving for variable 'w'.

Reorder the terms:
8 + -13 + -4w + -1w2 = 13 + w2 + -13 + -1w2

Combine like terms: 8 + -13 = -5
-5 + -4w + -1w2 = 13 + w2 + -13 + -1w2

Reorder the terms:
-5 + -4w + -1w2 = 13 + -13 + w2 + -1w2

Combine like terms: 13 + -13 = 0
-5 + -4w + -1w2 = 0 + w2 + -1w2
-5 + -4w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-5 + -4w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 4w + w2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 4w + w2)' equal to zero and attempt to solve:

Simplifying
5 + 4w + w2 = 0

Solving
5 + 4w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 4w + -5 + w2 = 0 + -5

Reorder the terms:
5 + -5 + 4w + w2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4w + w2 = 0 + -5
4w + w2 = 0 + -5

Combine like terms: 0 + -5 = -5
4w + w2 = -5

The w term is 4w.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4w + 4 + w2 = -5 + 4

Reorder the terms:
4 + 4w + w2 = -5 + 4

Combine like terms: -5 + 4 = -1
4 + 4w + w2 = -1

Factor a perfect square on the left side:
(w + 2)(w + 2) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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