w^2=2w^2+8w+36

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Solution for w^2=2w^2+8w+36 equation: 


Simplifying
w2 = 2w2 + 8w + 36

Reorder the terms:
w2 = 36 + 8w + 2w2

Solving
w2 = 36 + 8w + 2w2

Solving for variable 'w'.

Reorder the terms:
-36 + -8w + w2 + -2w2 = 36 + 8w + 2w2 + -36 + -8w + -2w2

Combine like terms: w2 + -2w2 = -1w2
-36 + -8w + -1w2 = 36 + 8w + 2w2 + -36 + -8w + -2w2

Reorder the terms:
-36 + -8w + -1w2 = 36 + -36 + 8w + -8w + 2w2 + -2w2

Combine like terms: 36 + -36 = 0
-36 + -8w + -1w2 = 0 + 8w + -8w + 2w2 + -2w2
-36 + -8w + -1w2 = 8w + -8w + 2w2 + -2w2

Combine like terms: 8w + -8w = 0
-36 + -8w + -1w2 = 0 + 2w2 + -2w2
-36 + -8w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-36 + -8w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(36 + 8w + w2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(36 + 8w + w2)' equal to zero and attempt to solve:

Simplifying
36 + 8w + w2 = 0

Solving
36 + 8w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 8w + -36 + w2 = 0 + -36

Reorder the terms:
36 + -36 + 8w + w2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 8w + w2 = 0 + -36
8w + w2 = 0 + -36

Combine like terms: 0 + -36 = -36
8w + w2 = -36

The w term is 8w.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8w + 16 + w2 = -36 + 16

Reorder the terms:
16 + 8w + w2 = -36 + 16

Combine like terms: -36 + 16 = -20
16 + 8w + w2 = -20

Factor a perfect square on the left side:
(w + 4)(w + 4) = -20

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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