w^2+11w-320=0

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Solution for w^2+11w-320=0 equation: 


Simplifying
w2 + 11w + -320 = 0

Reorder the terms:
-320 + 11w + w2 = 0

Solving
-320 + 11w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '320' to each side of the equation.
-320 + 11w + 320 + w2 = 0 + 320

Reorder the terms:
-320 + 320 + 11w + w2 = 0 + 320

Combine like terms: -320 + 320 = 0
0 + 11w + w2 = 0 + 320
11w + w2 = 0 + 320

Combine like terms: 0 + 320 = 320
11w + w2 = 320

The w term is 11w.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11w + 30.25 + w2 = 320 + 30.25

Reorder the terms:
30.25 + 11w + w2 = 320 + 30.25

Combine like terms: 320 + 30.25 = 350.25
30.25 + 11w + w2 = 350.25

Factor a perfect square on the left side:
(w + 5.5)(w + 5.5) = 350.25

Calculate the square root of the right side: 18.714967272

Break this problem into two subproblems by setting 
(w + 5.5) equal to 18.714967272 and -18.714967272.


Subproblem 1
w + 5.5 = 18.714967272

Simplifying
w + 5.5 = 18.714967272

Reorder the terms:
5.5 + w = 18.714967272

Solving
5.5 + w = 18.714967272

Solving for variable 'w'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + w = 18.714967272 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + w = 18.714967272 + -5.5
w = 18.714967272 + -5.5

Combine like terms: 18.714967272 + -5.5 = 13.214967272
w = 13.214967272

Simplifying
w = 13.214967272


Subproblem 2
w + 5.5 = -18.714967272

Simplifying
w + 5.5 = -18.714967272

Reorder the terms:
5.5 + w = -18.714967272

Solving
5.5 + w = -18.714967272

Solving for variable 'w'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + w = -18.714967272 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + w = -18.714967272 + -5.5
w = -18.714967272 + -5.5

Combine like terms: -18.714967272 + -5.5 = -24.214967272
w = -24.214967272

Simplifying
w = -24.214967272


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {13.214967272, -24.214967272}

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