w^2+10w-880=0

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Solution for w^2+10w-880=0 equation: 


Simplifying
w2 + 10w + -880 = 0

Reorder the terms:
-880 + 10w + w2 = 0

Solving
-880 + 10w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '880' to each side of the equation.
-880 + 10w + 880 + w2 = 0 + 880

Reorder the terms:
-880 + 880 + 10w + w2 = 0 + 880

Combine like terms: -880 + 880 = 0
0 + 10w + w2 = 0 + 880
10w + w2 = 0 + 880

Combine like terms: 0 + 880 = 880
10w + w2 = 880

The w term is 10w.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10w + 25 + w2 = 880 + 25

Reorder the terms:
25 + 10w + w2 = 880 + 25

Combine like terms: 880 + 25 = 905
25 + 10w + w2 = 905

Factor a perfect square on the left side:
(w + 5)(w + 5) = 905

Calculate the square root of the right side: 30.083217913

Break this problem into two subproblems by setting 
(w + 5) equal to 30.083217913 and -30.083217913.


Subproblem 1
w + 5 = 30.083217913

Simplifying
w + 5 = 30.083217913

Reorder the terms:
5 + w = 30.083217913

Solving
5 + w = 30.083217913

Solving for variable 'w'.

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

Add '-5' to each side of the equation.
5 + -5 + w = 30.083217913 + -5

Combine like terms: 5 + -5 = 0
0 + w = 30.083217913 + -5
w = 30.083217913 + -5

Combine like terms: 30.083217913 + -5 = 25.083217913
w = 25.083217913

Simplifying
w = 25.083217913


Subproblem 2
w + 5 = -30.083217913

Simplifying
w + 5 = -30.083217913

Reorder the terms:
5 + w = -30.083217913

Solving
5 + w = -30.083217913

Solving for variable 'w'.

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

Add '-5' to each side of the equation.
5 + -5 + w = -30.083217913 + -5

Combine like terms: 5 + -5 = 0
0 + w = -30.083217913 + -5
w = -30.083217913 + -5

Combine like terms: -30.083217913 + -5 = -35.083217913
w = -35.083217913

Simplifying
w = -35.083217913


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {25.083217913, -35.083217913}

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