64=(3w+8)w

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Solution for 64=(3w+8)w equation: 


Simplifying
64 = (3w + 8) * w

Reorder the terms:
64 = (8 + 3w) * w

Reorder the terms for easier multiplication:
64 = w(8 + 3w)
64 = (8 * w + 3w * w)
64 = (8w + 3w2)

Solving
64 = 8w + 3w2

Solving for variable 'w'.

Reorder the terms:
64 + -8w + -3w2 = 8w + -8w + 3w2 + -3w2

Combine like terms: 8w + -8w = 0
64 + -8w + -3w2 = 0 + 3w2 + -3w2
64 + -8w + -3w2 = 3w2 + -3w2

Combine like terms: 3w2 + -3w2 = 0
64 + -8w + -3w2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-21.33333333 + 2.666666667w + w2 = 0

Move the constant term to the right:

Add '21.33333333' to each side of the equation.
-21.33333333 + 2.666666667w + 21.33333333 + w2 = 0 + 21.33333333

Reorder the terms:
-21.33333333 + 21.33333333 + 2.666666667w + w2 = 0 + 21.33333333

Combine like terms: -21.33333333 + 21.33333333 = 0.00000000
0.00000000 + 2.666666667w + w2 = 0 + 21.33333333
2.666666667w + w2 = 0 + 21.33333333

Combine like terms: 0 + 21.33333333 = 21.33333333
2.666666667w + w2 = 21.33333333

The w term is 2.666666667w.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667w + 1.777777780 + w2 = 21.33333333 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667w + w2 = 21.33333333 + 1.777777780

Combine like terms: 21.33333333 + 1.777777780 = 23.11111111
1.777777780 + 2.666666667w + w2 = 23.11111111

Factor a perfect square on the left side:
(w + 1.333333334)(w + 1.333333334) = 23.11111111

Calculate the square root of the right side: 4.807401701

Break this problem into two subproblems by setting 
(w + 1.333333334) equal to 4.807401701 and -4.807401701.


Subproblem 1
w + 1.333333334 = 4.807401701

Simplifying
w + 1.333333334 = 4.807401701

Reorder the terms:
1.333333334 + w = 4.807401701

Solving
1.333333334 + w = 4.807401701

Solving for variable 'w'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + w = 4.807401701 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + w = 4.807401701 + -1.333333334
w = 4.807401701 + -1.333333334

Combine like terms: 4.807401701 + -1.333333334 = 3.474068367
w = 3.474068367

Simplifying
w = 3.474068367


Subproblem 2
w + 1.333333334 = -4.807401701

Simplifying
w + 1.333333334 = -4.807401701

Reorder the terms:
1.333333334 + w = -4.807401701

Solving
1.333333334 + w = -4.807401701

Solving for variable 'w'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + w = -4.807401701 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + w = -4.807401701 + -1.333333334
w = -4.807401701 + -1.333333334

Combine like terms: -4.807401701 + -1.333333334 = -6.140735035
w = -6.140735035

Simplifying
w = -6.140735035


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.474068367, -6.140735035}

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