3w^2-18w-20=0

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Solution for 3w^2-18w-20=0 equation: 


Simplifying
3w2 + -18w + -20 = 0

Reorder the terms:
-20 + -18w + 3w2 = 0

Solving
-20 + -18w + 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'.
-6.666666667 + -6w + w2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + -6w + 6.666666667 + w2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + -6w + w2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + -6w + w2 = 0 + 6.666666667
-6w + w2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
-6w + w2 = 6.666666667

The w term is -6w.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6w + 9 + w2 = 6.666666667 + 9

Reorder the terms:
9 + -6w + w2 = 6.666666667 + 9

Combine like terms: 6.666666667 + 9 = 15.666666667
9 + -6w + w2 = 15.666666667

Factor a perfect square on the left side:
(w + -3)(w + -3) = 15.666666667

Calculate the square root of the right side: 3.958114029

Break this problem into two subproblems by setting 
(w + -3) equal to 3.958114029 and -3.958114029.


Subproblem 1
w + -3 = 3.958114029

Simplifying
w + -3 = 3.958114029

Reorder the terms:
-3 + w = 3.958114029

Solving
-3 + w = 3.958114029

Solving for variable 'w'.

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

Add '3' to each side of the equation.
-3 + 3 + w = 3.958114029 + 3

Combine like terms: -3 + 3 = 0
0 + w = 3.958114029 + 3
w = 3.958114029 + 3

Combine like terms: 3.958114029 + 3 = 6.958114029
w = 6.958114029

Simplifying
w = 6.958114029


Subproblem 2
w + -3 = -3.958114029

Simplifying
w + -3 = -3.958114029

Reorder the terms:
-3 + w = -3.958114029

Solving
-3 + w = -3.958114029

Solving for variable 'w'.

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

Add '3' to each side of the equation.
-3 + 3 + w = -3.958114029 + 3

Combine like terms: -3 + 3 = 0
0 + w = -3.958114029 + 3
w = -3.958114029 + 3

Combine like terms: -3.958114029 + 3 = -0.958114029
w = -0.958114029

Simplifying
w = -0.958114029


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.958114029, -0.958114029}

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