-3w^2+3w+50=0

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Solution for -3w^2+3w+50=0 equation: 


Simplifying
-3w2 + 3w + 50 = 0

Reorder the terms:
50 + 3w + -3w2 = 0

Solving
50 + 3w + -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'.
-16.66666667 + -1w + w2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + -1w + 16.66666667 + w2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + -1w + w2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + -1w + w2 = 0 + 16.66666667
-1w + w2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
-1w + w2 = 16.66666667

The w term is -1w.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1w + 0.25 + w2 = 16.66666667 + 0.25

Reorder the terms:
0.25 + -1w + w2 = 16.66666667 + 0.25

Combine like terms: 16.66666667 + 0.25 = 16.91666667
0.25 + -1w + w2 = 16.91666667

Factor a perfect square on the left side:
(w + -0.5)(w + -0.5) = 16.91666667

Calculate the square root of the right side: 4.11298756

Break this problem into two subproblems by setting 
(w + -0.5) equal to 4.11298756 and -4.11298756.


Subproblem 1
w + -0.5 = 4.11298756

Simplifying
w + -0.5 = 4.11298756

Reorder the terms:
-0.5 + w = 4.11298756

Solving
-0.5 + w = 4.11298756

Solving for variable 'w'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + w = 4.11298756 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + w = 4.11298756 + 0.5
w = 4.11298756 + 0.5

Combine like terms: 4.11298756 + 0.5 = 4.61298756
w = 4.61298756

Simplifying
w = 4.61298756


Subproblem 2
w + -0.5 = -4.11298756

Simplifying
w + -0.5 = -4.11298756

Reorder the terms:
-0.5 + w = -4.11298756

Solving
-0.5 + w = -4.11298756

Solving for variable 'w'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + w = -4.11298756 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + w = -4.11298756 + 0.5
w = -4.11298756 + 0.5

Combine like terms: -4.11298756 + 0.5 = -3.61298756
w = -3.61298756

Simplifying
w = -3.61298756


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.61298756, -3.61298756}

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