w^2+6w-71=0

Solution for w^2+6w-71=0 equation:

Simplifying
w2 + 6w + -71 = 0

Reorder the terms:
-71 + 6w + w2 = 0

Solving
-71 + 6w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '71' to each side of the equation.
-71 + 6w + 71 + w2 = 0 + 71

Reorder the terms:
-71 + 71 + 6w + w2 = 0 + 71

Combine like terms: -71 + 71 = 0
0 + 6w + w2 = 0 + 71
6w + w2 = 0 + 71

Combine like terms: 0 + 71 = 71
6w + w2 = 71

The w term is 6w.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6w + 9 + w2 = 71 + 9

Reorder the terms:
9 + 6w + w2 = 71 + 9

Combine like terms: 71 + 9 = 80
9 + 6w + w2 = 80

Factor a perfect square on the left side:
(w + 3)(w + 3) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(w + 3) equal to 8.94427191 and -8.94427191.

Subproblem 1
w + 3 = 8.94427191

Simplifying
w + 3 = 8.94427191

Reorder the terms:
3 + w = 8.94427191

Solving
3 + w = 8.94427191

Solving for variable 'w'.

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

Add '-3' to each side of the equation.
3 + -3 + w = 8.94427191 + -3

Combine like terms: 3 + -3 = 0
0 + w = 8.94427191 + -3
w = 8.94427191 + -3

Combine like terms: 8.94427191 + -3 = 5.94427191
w = 5.94427191

Simplifying
w = 5.94427191

Subproblem 2
w + 3 = -8.94427191

Simplifying
w + 3 = -8.94427191

Reorder the terms:
3 + w = -8.94427191

Solving
3 + w = -8.94427191

Solving for variable 'w'.

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

Add '-3' to each side of the equation.
3 + -3 + w = -8.94427191 + -3

Combine like terms: 3 + -3 = 0
0 + w = -8.94427191 + -3
w = -8.94427191 + -3

Combine like terms: -8.94427191 + -3 = -11.94427191
w = -11.94427191

Simplifying
w = -11.94427191

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.94427191, -11.94427191}