w^2+4w-35=0

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Solution for w^2+4w-35=0 equation: 


Simplifying
w2 + 4w + -35 = 0

Reorder the terms:
-35 + 4w + w2 = 0

Solving
-35 + 4w + 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 + 4w + 35 + w2 = 0 + 35

Reorder the terms:
-35 + 35 + 4w + w2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 4w + w2 = 0 + 35
4w + w2 = 0 + 35

Combine like terms: 0 + 35 = 35
4w + w2 = 35

The w term is 4w.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4w + 4 + w2 = 35 + 4

Reorder the terms:
4 + 4w + w2 = 35 + 4

Combine like terms: 35 + 4 = 39
4 + 4w + w2 = 39

Factor a perfect square on the left side:
(w + 2)(w + 2) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(w + 2) equal to 6.244997998 and -6.244997998.


Subproblem 1
w + 2 = 6.244997998

Simplifying
w + 2 = 6.244997998

Reorder the terms:
2 + w = 6.244997998

Solving
2 + w = 6.244997998

Solving for variable 'w'.

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

Add '-2' to each side of the equation.
2 + -2 + w = 6.244997998 + -2

Combine like terms: 2 + -2 = 0
0 + w = 6.244997998 + -2
w = 6.244997998 + -2

Combine like terms: 6.244997998 + -2 = 4.244997998
w = 4.244997998

Simplifying
w = 4.244997998


Subproblem 2
w + 2 = -6.244997998

Simplifying
w + 2 = -6.244997998

Reorder the terms:
2 + w = -6.244997998

Solving
2 + w = -6.244997998

Solving for variable 'w'.

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

Add '-2' to each side of the equation.
2 + -2 + w = -6.244997998 + -2

Combine like terms: 2 + -2 = 0
0 + w = -6.244997998 + -2
w = -6.244997998 + -2

Combine like terms: -6.244997998 + -2 = -8.244997998
w = -8.244997998

Simplifying
w = -8.244997998


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.244997998, -8.244997998}

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