w^2+3w-85=0

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Solution for w^2+3w-85=0 equation: 


Simplifying
w2 + 3w + -85 = 0

Reorder the terms:
-85 + 3w + w2 = 0

Solving
-85 + 3w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + 3w + 85 + w2 = 0 + 85

Reorder the terms:
-85 + 85 + 3w + w2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + 3w + w2 = 0 + 85
3w + w2 = 0 + 85

Combine like terms: 0 + 85 = 85
3w + w2 = 85

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = 85 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 85 + 2.25

Combine like terms: 85 + 2.25 = 87.25
2.25 + 3w + w2 = 87.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 87.25

Calculate the square root of the right side: 9.340770846

Break this problem into two subproblems by setting 
(w + 1.5) equal to 9.340770846 and -9.340770846.


Subproblem 1
w + 1.5 = 9.340770846

Simplifying
w + 1.5 = 9.340770846

Reorder the terms:
1.5 + w = 9.340770846

Solving
1.5 + w = 9.340770846

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = 9.340770846 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 9.340770846 + -1.5
w = 9.340770846 + -1.5

Combine like terms: 9.340770846 + -1.5 = 7.840770846
w = 7.840770846

Simplifying
w = 7.840770846


Subproblem 2
w + 1.5 = -9.340770846

Simplifying
w + 1.5 = -9.340770846

Reorder the terms:
1.5 + w = -9.340770846

Solving
1.5 + w = -9.340770846

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = -9.340770846 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -9.340770846 + -1.5
w = -9.340770846 + -1.5

Combine like terms: -9.340770846 + -1.5 = -10.840770846
w = -10.840770846

Simplifying
w = -10.840770846


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.840770846, -10.840770846}

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