w(2w-8)=126

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Solution for w(2w-8)=126 equation:


Simplifying
w(2w + -8) = 126

Reorder the terms:
w(-8 + 2w) = 126
(-8 * w + 2w * w) = 126
(-8w + 2w2) = 126

Solving
-8w + 2w2 = 126

Solving for variable 'w'.

Reorder the terms:
-126 + -8w + 2w2 = 126 + -126

Combine like terms: 126 + -126 = 0
-126 + -8w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-63 + -4w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-63 + -4w + w2)' equal to zero and attempt to solve:

Simplifying
-63 + -4w + w2 = 0

Solving
-63 + -4w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '63' to each side of the equation.
-63 + -4w + 63 + w2 = 0 + 63

Reorder the terms:
-63 + 63 + -4w + w2 = 0 + 63

Combine like terms: -63 + 63 = 0
0 + -4w + w2 = 0 + 63
-4w + w2 = 0 + 63

Combine like terms: 0 + 63 = 63
-4w + w2 = 63

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 = 63 + 4

Reorder the terms:
4 + -4w + w2 = 63 + 4

Combine like terms: 63 + 4 = 67
4 + -4w + w2 = 67

Factor a perfect square on the left side:
(w + -2)(w + -2) = 67

Calculate the square root of the right side: 8.185352772

Break this problem into two subproblems by setting 
(w + -2) equal to 8.185352772 and -8.185352772.


Subproblem 1
w + -2 = 8.185352772

Simplifying
w + -2 = 8.185352772

Reorder the terms:
-2 + w = 8.185352772

Solving
-2 + w = 8.185352772

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + w = 8.185352772 + 2

Combine like terms: -2 + 2 = 0
0 + w = 8.185352772 + 2
w = 8.185352772 + 2

Combine like terms: 8.185352772 + 2 = 10.185352772
w = 10.185352772

Simplifying
w = 10.185352772


Subproblem 2
w + -2 = -8.185352772

Simplifying
w + -2 = -8.185352772

Reorder the terms:
-2 + w = -8.185352772

Solving
-2 + w = -8.185352772

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + w = -8.185352772 + 2

Combine like terms: -2 + 2 = 0
0 + w = -8.185352772 + 2
w = -8.185352772 + 2

Combine like terms: -8.185352772 + 2 = -6.185352772
w = -6.185352772

Simplifying
w = -6.185352772


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {10.185352772, -6.185352772}
Solution
w = {10.185352772, -6.185352772}

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