w^2+5w-35=0

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Solution for w^2+5w-35=0 equation: 


Simplifying
w2 + 5w + -35 = 0

Reorder the terms:
-35 + 5w + w2 = 0

Solving
-35 + 5w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 5w + 35 + w2 = 0 + 35

Reorder the terms:
-35 + 35 + 5w + w2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 5w + w2 = 0 + 35
5w + w2 = 0 + 35

Combine like terms: 0 + 35 = 35
5w + w2 = 35

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = 35 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 35 + 6.25

Combine like terms: 35 + 6.25 = 41.25
6.25 + 5w + w2 = 41.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(w + 2.5) equal to 6.422616289 and -6.422616289.


Subproblem 1
w + 2.5 = 6.422616289

Simplifying
w + 2.5 = 6.422616289

Reorder the terms:
2.5 + w = 6.422616289

Solving
2.5 + w = 6.422616289

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = 6.422616289 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 6.422616289 + -2.5
w = 6.422616289 + -2.5

Combine like terms: 6.422616289 + -2.5 = 3.922616289
w = 3.922616289

Simplifying
w = 3.922616289


Subproblem 2
w + 2.5 = -6.422616289

Simplifying
w + 2.5 = -6.422616289

Reorder the terms:
2.5 + w = -6.422616289

Solving
2.5 + w = -6.422616289

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = -6.422616289 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -6.422616289 + -2.5
w = -6.422616289 + -2.5

Combine like terms: -6.422616289 + -2.5 = -8.922616289
w = -8.922616289

Simplifying
w = -8.922616289


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.922616289, -8.922616289}

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