w^2+10w-236=0

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Solution for w^2+10w-236=0 equation: 


Simplifying
w2 + 10w + -236 = 0

Reorder the terms:
-236 + 10w + w2 = 0

Solving
-236 + 10w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '236' to each side of the equation.
-236 + 10w + 236 + w2 = 0 + 236

Reorder the terms:
-236 + 236 + 10w + w2 = 0 + 236

Combine like terms: -236 + 236 = 0
0 + 10w + w2 = 0 + 236
10w + w2 = 0 + 236

Combine like terms: 0 + 236 = 236
10w + w2 = 236

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 = 236 + 25

Reorder the terms:
25 + 10w + w2 = 236 + 25

Combine like terms: 236 + 25 = 261
25 + 10w + w2 = 261

Factor a perfect square on the left side:
(w + 5)(w + 5) = 261

Calculate the square root of the right side: 16.155494421

Break this problem into two subproblems by setting 
(w + 5) equal to 16.155494421 and -16.155494421.


Subproblem 1
w + 5 = 16.155494421

Simplifying
w + 5 = 16.155494421

Reorder the terms:
5 + w = 16.155494421

Solving
5 + w = 16.155494421

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 = 16.155494421 + -5

Combine like terms: 5 + -5 = 0
0 + w = 16.155494421 + -5
w = 16.155494421 + -5

Combine like terms: 16.155494421 + -5 = 11.155494421
w = 11.155494421

Simplifying
w = 11.155494421


Subproblem 2
w + 5 = -16.155494421

Simplifying
w + 5 = -16.155494421

Reorder the terms:
5 + w = -16.155494421

Solving
5 + w = -16.155494421

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 = -16.155494421 + -5

Combine like terms: 5 + -5 = 0
0 + w = -16.155494421 + -5
w = -16.155494421 + -5

Combine like terms: -16.155494421 + -5 = -21.155494421
w = -21.155494421

Simplifying
w = -21.155494421


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {11.155494421, -21.155494421}

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