(2w-2)(w-2)=-32

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Solution for (2w-2)(w-2)=-32 equation: 


Simplifying
(2w + -2)(w + -2) = -32

Reorder the terms:
(-2 + 2w)(w + -2) = -32

Reorder the terms:
(-2 + 2w)(-2 + w) = -32

Multiply (-2 + 2w) * (-2 + w)
(-2(-2 + w) + 2w * (-2 + w)) = -32
((-2 * -2 + w * -2) + 2w * (-2 + w)) = -32
((4 + -2w) + 2w * (-2 + w)) = -32
(4 + -2w + (-2 * 2w + w * 2w)) = -32
(4 + -2w + (-4w + 2w2)) = -32

Combine like terms: -2w + -4w = -6w
(4 + -6w + 2w2) = -32

Solving
4 + -6w + 2w2 = -32

Solving for variable 'w'.

Reorder the terms:
4 + 32 + -6w + 2w2 = -32 + 32

Combine like terms: 4 + 32 = 36
36 + -6w + 2w2 = -32 + 32

Combine like terms: -32 + 32 = 0
36 + -6w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + -3w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(18 + -3w + w2)' equal to zero and attempt to solve:

Simplifying
18 + -3w + w2 = 0

Solving
18 + -3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -3w + -18 + w2 = 0 + -18

Reorder the terms:
18 + -18 + -3w + w2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -3w + w2 = 0 + -18
-3w + w2 = 0 + -18

Combine like terms: 0 + -18 = -18
-3w + w2 = -18

The w term is -3w.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3w + 2.25 + w2 = -18 + 2.25

Reorder the terms:
2.25 + -3w + w2 = -18 + 2.25

Combine like terms: -18 + 2.25 = -15.75
2.25 + -3w + w2 = -15.75

Factor a perfect square on the left side:
(w + -1.5)(w + -1.5) = -15.75

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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