w^2+10w-18=0

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Solution for w^2+10w-18=0 equation: 


Simplifying
w2 + 10w + -18 = 0

Reorder the terms:
-18 + 10w + w2 = 0

Solving
-18 + 10w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 10w + 18 + w2 = 0 + 18

Reorder the terms:
-18 + 18 + 10w + w2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 10w + w2 = 0 + 18
10w + w2 = 0 + 18

Combine like terms: 0 + 18 = 18
10w + w2 = 18

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 = 18 + 25

Reorder the terms:
25 + 10w + w2 = 18 + 25

Combine like terms: 18 + 25 = 43
25 + 10w + w2 = 43

Factor a perfect square on the left side:
(w + 5)(w + 5) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(w + 5) equal to 6.557438524 and -6.557438524.


Subproblem 1
w + 5 = 6.557438524

Simplifying
w + 5 = 6.557438524

Reorder the terms:
5 + w = 6.557438524

Solving
5 + w = 6.557438524

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 = 6.557438524 + -5

Combine like terms: 5 + -5 = 0
0 + w = 6.557438524 + -5
w = 6.557438524 + -5

Combine like terms: 6.557438524 + -5 = 1.557438524
w = 1.557438524

Simplifying
w = 1.557438524


Subproblem 2
w + 5 = -6.557438524

Simplifying
w + 5 = -6.557438524

Reorder the terms:
5 + w = -6.557438524

Solving
5 + w = -6.557438524

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 = -6.557438524 + -5

Combine like terms: 5 + -5 = 0
0 + w = -6.557438524 + -5
w = -6.557438524 + -5

Combine like terms: -6.557438524 + -5 = -11.557438524
w = -11.557438524

Simplifying
w = -11.557438524


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.557438524, -11.557438524}

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