2-(w+2)(w+2)=8

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Solution for 2-(w+2)(w+2)=8 equation: 


Simplifying
2 + -1(w + 2)(w + 2) = 8

Reorder the terms:
2 + -1(2 + w)(w + 2) = 8

Reorder the terms:
2 + -1(2 + w)(2 + w) = 8

Multiply (2 + w) * (2 + w)
2 + -1(2(2 + w) + w(2 + w)) = 8
2 + -1((2 * 2 + w * 2) + w(2 + w)) = 8
2 + -1((4 + 2w) + w(2 + w)) = 8
2 + -1(4 + 2w + (2 * w + w * w)) = 8
2 + -1(4 + 2w + (2w + w2)) = 8

Combine like terms: 2w + 2w = 4w
2 + -1(4 + 4w + w2) = 8
2 + (4 * -1 + 4w * -1 + w2 * -1) = 8
2 + (-4 + -4w + -1w2) = 8

Combine like terms: 2 + -4 = -2
-2 + -4w + -1w2 = 8

Solving
-2 + -4w + -1w2 = 8

Solving for variable 'w'.

Reorder the terms:
-2 + -8 + -4w + -1w2 = 8 + -8

Combine like terms: -2 + -8 = -10
-10 + -4w + -1w2 = 8 + -8

Combine like terms: 8 + -8 = 0
-10 + -4w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 4w + w2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(10 + 4w + w2)' equal to zero and attempt to solve:

Simplifying
10 + 4w + w2 = 0

Solving
10 + 4w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 4w + -10 + w2 = 0 + -10

Reorder the terms:
10 + -10 + 4w + w2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 4w + w2 = 0 + -10
4w + w2 = 0 + -10

Combine like terms: 0 + -10 = -10
4w + w2 = -10

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 = -10 + 4

Reorder the terms:
4 + 4w + w2 = -10 + 4

Combine like terms: -10 + 4 = -6
4 + 4w + w2 = -6

Factor a perfect square on the left side:
(w + 2)(w + 2) = -6

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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