3w^2+20w-936=0

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Solution for 3w^2+20w-936=0 equation: 


Simplifying
3w2 + 20w + -936 = 0

Reorder the terms:
-936 + 20w + 3w2 = 0

Solving
-936 + 20w + 3w2 = 0

Solving for variable 'w'.

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

Divide each side by '3'.
-312 + 6.666666667w + w2 = 0

Move the constant term to the right:

Add '312' to each side of the equation.
-312 + 6.666666667w + 312 + w2 = 0 + 312

Reorder the terms:
-312 + 312 + 6.666666667w + w2 = 0 + 312

Combine like terms: -312 + 312 = 0
0 + 6.666666667w + w2 = 0 + 312
6.666666667w + w2 = 0 + 312

Combine like terms: 0 + 312 = 312
6.666666667w + w2 = 312

The w term is 6.666666667w.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667w + 11.11111112 + w2 = 312 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667w + w2 = 312 + 11.11111112

Combine like terms: 312 + 11.11111112 = 323.11111112
11.11111112 + 6.666666667w + w2 = 323.11111112

Factor a perfect square on the left side:
(w + 3.333333334)(w + 3.333333334) = 323.11111112

Calculate the square root of the right side: 17.975291684

Break this problem into two subproblems by setting 
(w + 3.333333334) equal to 17.975291684 and -17.975291684.


Subproblem 1
w + 3.333333334 = 17.975291684

Simplifying
w + 3.333333334 = 17.975291684

Reorder the terms:
3.333333334 + w = 17.975291684

Solving
3.333333334 + w = 17.975291684

Solving for variable 'w'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + w = 17.975291684 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + w = 17.975291684 + -3.333333334
w = 17.975291684 + -3.333333334

Combine like terms: 17.975291684 + -3.333333334 = 14.64195835
w = 14.64195835

Simplifying
w = 14.64195835


Subproblem 2
w + 3.333333334 = -17.975291684

Simplifying
w + 3.333333334 = -17.975291684

Reorder the terms:
3.333333334 + w = -17.975291684

Solving
3.333333334 + w = -17.975291684

Solving for variable 'w'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + w = -17.975291684 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + w = -17.975291684 + -3.333333334
w = -17.975291684 + -3.333333334

Combine like terms: -17.975291684 + -3.333333334 = -21.308625018
w = -21.308625018

Simplifying
w = -21.308625018


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {14.64195835, -21.308625018}

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