9w^2-39w-50=0

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Solution for 9w^2-39w-50=0 equation: 


Simplifying
9w2 + -39w + -50 = 0

Reorder the terms:
-50 + -39w + 9w2 = 0

Solving
-50 + -39w + 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'.
-5.555555556 + -4.333333333w + w2 = 0

Move the constant term to the right:

Add '5.555555556' to each side of the equation.
-5.555555556 + -4.333333333w + 5.555555556 + w2 = 0 + 5.555555556

Reorder the terms:
-5.555555556 + 5.555555556 + -4.333333333w + w2 = 0 + 5.555555556

Combine like terms: -5.555555556 + 5.555555556 = 0.000000000
0.000000000 + -4.333333333w + w2 = 0 + 5.555555556
-4.333333333w + w2 = 0 + 5.555555556

Combine like terms: 0 + 5.555555556 = 5.555555556
-4.333333333w + w2 = 5.555555556

The w term is -4.333333333w.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333w + 4.694444446 + w2 = 5.555555556 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333w + w2 = 5.555555556 + 4.694444446

Combine like terms: 5.555555556 + 4.694444446 = 10.250000002
4.694444446 + -4.333333333w + w2 = 10.250000002

Factor a perfect square on the left side:
(w + -2.166666667)(w + -2.166666667) = 10.250000002

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(w + -2.166666667) equal to 3.201562119 and -3.201562119.


Subproblem 1
w + -2.166666667 = 3.201562119

Simplifying
w + -2.166666667 = 3.201562119

Reorder the terms:
-2.166666667 + w = 3.201562119

Solving
-2.166666667 + w = 3.201562119

Solving for variable 'w'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + w = 3.201562119 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + w = 3.201562119 + 2.166666667
w = 3.201562119 + 2.166666667

Combine like terms: 3.201562119 + 2.166666667 = 5.368228786
w = 5.368228786

Simplifying
w = 5.368228786


Subproblem 2
w + -2.166666667 = -3.201562119

Simplifying
w + -2.166666667 = -3.201562119

Reorder the terms:
-2.166666667 + w = -3.201562119

Solving
-2.166666667 + w = -3.201562119

Solving for variable 'w'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + w = -3.201562119 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + w = -3.201562119 + 2.166666667
w = -3.201562119 + 2.166666667

Combine like terms: -3.201562119 + 2.166666667 = -1.034895452
w = -1.034895452

Simplifying
w = -1.034895452


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.368228786, -1.034895452}

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