w^2+7w=-2

Solution for w^2+7w=-2 equation:

Simplifying
w2 + 7w = -2

Reorder the terms:
7w + w2 = -2

Solving
7w + w2 = -2

Solving for variable 'w'.

Reorder the terms:
2 + 7w + w2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 7w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 7w + -2 + w2 = 0 + -2

Reorder the terms:
2 + -2 + 7w + w2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7w + w2 = 0 + -2
7w + w2 = 0 + -2

Combine like terms: 0 + -2 = -2
7w + w2 = -2

The w term is 7w.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7w + 12.25 + w2 = -2 + 12.25

Reorder the terms:
12.25 + 7w + w2 = -2 + 12.25

Combine like terms: -2 + 12.25 = 10.25
12.25 + 7w + w2 = 10.25

Factor a perfect square on the left side:
(w + 3.5)(w + 3.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(w + 3.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
w + 3.5 = 3.201562119

Simplifying
w + 3.5 = 3.201562119

Reorder the terms:
3.5 + w = 3.201562119

Solving
3.5 + w = 3.201562119

Solving for variable 'w'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + w = 3.201562119 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + w = 3.201562119 + -3.5
w = 3.201562119 + -3.5

Combine like terms: 3.201562119 + -3.5 = -0.298437881
w = -0.298437881

Simplifying
w = -0.298437881

Subproblem 2
w + 3.5 = -3.201562119

Simplifying
w + 3.5 = -3.201562119

Reorder the terms:
3.5 + w = -3.201562119

Solving
3.5 + w = -3.201562119

Solving for variable 'w'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + w = -3.201562119 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + w = -3.201562119 + -3.5
w = -3.201562119 + -3.5

Combine like terms: -3.201562119 + -3.5 = -6.701562119
w = -6.701562119

Simplifying
w = -6.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.298437881, -6.701562119}