9w^2-48w-64=0

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Solution for 9w^2-48w-64=0 equation: 


Simplifying
9w2 + -48w + -64 = 0

Reorder the terms:
-64 + -48w + 9w2 = 0

Solving
-64 + -48w + 9w2 = 0

Solving for variable 'w'.

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

Divide each side by '9'.
-7.111111111 + -5.333333333w + w2 = 0

Move the constant term to the right:

Add '7.111111111' to each side of the equation.
-7.111111111 + -5.333333333w + 7.111111111 + w2 = 0 + 7.111111111

Reorder the terms:
-7.111111111 + 7.111111111 + -5.333333333w + w2 = 0 + 7.111111111

Combine like terms: -7.111111111 + 7.111111111 = 0.000000000
0.000000000 + -5.333333333w + w2 = 0 + 7.111111111
-5.333333333w + w2 = 0 + 7.111111111

Combine like terms: 0 + 7.111111111 = 7.111111111
-5.333333333w + w2 = 7.111111111

The w term is -5.333333333w.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333w + 7.111111113 + w2 = 7.111111111 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333w + w2 = 7.111111111 + 7.111111113

Combine like terms: 7.111111111 + 7.111111113 = 14.222222224
7.111111113 + -5.333333333w + w2 = 14.222222224

Factor a perfect square on the left side:
(w + -2.666666667)(w + -2.666666667) = 14.222222224

Calculate the square root of the right side: 3.771236167

Break this problem into two subproblems by setting 
(w + -2.666666667) equal to 3.771236167 and -3.771236167.


Subproblem 1
w + -2.666666667 = 3.771236167

Simplifying
w + -2.666666667 = 3.771236167

Reorder the terms:
-2.666666667 + w = 3.771236167

Solving
-2.666666667 + w = 3.771236167

Solving for variable 'w'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + w = 3.771236167 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + w = 3.771236167 + 2.666666667
w = 3.771236167 + 2.666666667

Combine like terms: 3.771236167 + 2.666666667 = 6.437902834
w = 6.437902834

Simplifying
w = 6.437902834


Subproblem 2
w + -2.666666667 = -3.771236167

Simplifying
w + -2.666666667 = -3.771236167

Reorder the terms:
-2.666666667 + w = -3.771236167

Solving
-2.666666667 + w = -3.771236167

Solving for variable 'w'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + w = -3.771236167 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + w = -3.771236167 + 2.666666667
w = -3.771236167 + 2.666666667

Combine like terms: -3.771236167 + 2.666666667 = -1.1045695
w = -1.1045695

Simplifying
w = -1.1045695


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.437902834, -1.1045695}

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