2w^2+38w-90=0

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Solution for 2w^2+38w-90=0 equation: 


Simplifying
2w2 + 38w + -90 = 0

Reorder the terms:
-90 + 38w + 2w2 = 0

Solving
-90 + 38w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 19w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + 19w + w2)' equal to zero and attempt to solve:

Simplifying
-45 + 19w + w2 = 0

Solving
-45 + 19w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 19w + 45 + w2 = 0 + 45

Reorder the terms:
-45 + 45 + 19w + w2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 19w + w2 = 0 + 45
19w + w2 = 0 + 45

Combine like terms: 0 + 45 = 45
19w + w2 = 45

The w term is 19w.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19w + 90.25 + w2 = 45 + 90.25

Reorder the terms:
90.25 + 19w + w2 = 45 + 90.25

Combine like terms: 45 + 90.25 = 135.25
90.25 + 19w + w2 = 135.25

Factor a perfect square on the left side:
(w + 9.5)(w + 9.5) = 135.25

Calculate the square root of the right side: 11.62970335

Break this problem into two subproblems by setting 
(w + 9.5) equal to 11.62970335 and -11.62970335.


Subproblem 1
w + 9.5 = 11.62970335

Simplifying
w + 9.5 = 11.62970335

Reorder the terms:
9.5 + w = 11.62970335

Solving
9.5 + w = 11.62970335

Solving for variable 'w'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + w = 11.62970335 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + w = 11.62970335 + -9.5
w = 11.62970335 + -9.5

Combine like terms: 11.62970335 + -9.5 = 2.12970335
w = 2.12970335

Simplifying
w = 2.12970335


Subproblem 2
w + 9.5 = -11.62970335

Simplifying
w + 9.5 = -11.62970335

Reorder the terms:
9.5 + w = -11.62970335

Solving
9.5 + w = -11.62970335

Solving for variable 'w'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + w = -11.62970335 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + w = -11.62970335 + -9.5
w = -11.62970335 + -9.5

Combine like terms: -11.62970335 + -9.5 = -21.12970335
w = -21.12970335

Simplifying
w = -21.12970335


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.12970335, -21.12970335}
Solution
w = {2.12970335, -21.12970335}

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