(w)(2w+8)2=26.25

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Solution for (w)(2w+8)2=26.25 equation: 


Simplifying
(w)(2w + 8) * 2 = 26.25

Reorder the terms:
w(8 + 2w) * 2 = 26.25

Reorder the terms for easier multiplication:
2w(8 + 2w) = 26.25
(8 * 2w + 2w * 2w) = 26.25
(16w + 4w2) = 26.25

Solving
16w + 4w2 = 26.25

Solving for variable 'w'.

Reorder the terms:
-26.25 + 16w + 4w2 = 26.25 + -26.25

Combine like terms: 26.25 + -26.25 = 0.00
-26.25 + 16w + 4w2 = 0.00

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-6.5625 + 4w + w2 = 0.00

Move the constant term to the right:

Add '6.5625' to each side of the equation.
-6.5625 + 4w + 6.5625 + w2 = 0.00 + 6.5625

Reorder the terms:
-6.5625 + 6.5625 + 4w + w2 = 0.00 + 6.5625

Combine like terms: -6.5625 + 6.5625 = 0.0000
0.0000 + 4w + w2 = 0.00 + 6.5625
4w + w2 = 0.00 + 6.5625

Combine like terms: 0.00 + 6.5625 = 6.5625
4w + w2 = 6.5625

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 = 6.5625 + 4

Reorder the terms:
4 + 4w + w2 = 6.5625 + 4

Combine like terms: 6.5625 + 4 = 10.5625
4 + 4w + w2 = 10.5625

Factor a perfect square on the left side:
(w + 2)(w + 2) = 10.5625

Calculate the square root of the right side: 3.25

Break this problem into two subproblems by setting 
(w + 2) equal to 3.25 and -3.25.


Subproblem 1
w + 2 = 3.25

Simplifying
w + 2 = 3.25

Reorder the terms:
2 + w = 3.25

Solving
2 + w = 3.25

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 = 3.25 + -2

Combine like terms: 2 + -2 = 0
0 + w = 3.25 + -2
w = 3.25 + -2

Combine like terms: 3.25 + -2 = 1.25
w = 1.25

Simplifying
w = 1.25


Subproblem 2
w + 2 = -3.25

Simplifying
w + 2 = -3.25

Reorder the terms:
2 + w = -3.25

Solving
2 + w = -3.25

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 = -3.25 + -2

Combine like terms: 2 + -2 = 0
0 + w = -3.25 + -2
w = -3.25 + -2

Combine like terms: -3.25 + -2 = -5.25
w = -5.25

Simplifying
w = -5.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.25, -5.25}

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