2w^2+w-32=0

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Solution for 2w^2+w-32=0 equation: 


Simplifying
2w2 + w + -32 = 0

Reorder the terms:
-32 + w + 2w2 = 0

Solving
-32 + w + 2w2 = 0

Solving for variable 'w'.

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

Divide each side by '2'.
-16 + 0.5w + w2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 0.5w + 16 + w2 = 0 + 16

Reorder the terms:
-16 + 16 + 0.5w + w2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 0.5w + w2 = 0 + 16
0.5w + w2 = 0 + 16

Combine like terms: 0 + 16 = 16
0.5w + w2 = 16

The w term is w.  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.
0.5w + 0.25 + w2 = 16 + 0.25

Reorder the terms:
0.25 + 0.5w + w2 = 16 + 0.25

Combine like terms: 16 + 0.25 = 16.25
0.25 + 0.5w + w2 = 16.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(w + 0.5) equal to 4.031128874 and -4.031128874.


Subproblem 1
w + 0.5 = 4.031128874

Simplifying
w + 0.5 = 4.031128874

Reorder the terms:
0.5 + w = 4.031128874

Solving
0.5 + w = 4.031128874

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 = 4.031128874 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 4.031128874 + -0.5
w = 4.031128874 + -0.5

Combine like terms: 4.031128874 + -0.5 = 3.531128874
w = 3.531128874

Simplifying
w = 3.531128874


Subproblem 2
w + 0.5 = -4.031128874

Simplifying
w + 0.5 = -4.031128874

Reorder the terms:
0.5 + w = -4.031128874

Solving
0.5 + w = -4.031128874

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 = -4.031128874 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -4.031128874 + -0.5
w = -4.031128874 + -0.5

Combine like terms: -4.031128874 + -0.5 = -4.531128874
w = -4.531128874

Simplifying
w = -4.531128874


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.531128874, -4.531128874}

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