w^2+2w-11=0

Solution for w^2+2w-11=0 equation:

Simplifying
w2 + 2w + -11 = 0

Reorder the terms:
-11 + 2w + w2 = 0

Solving
-11 + 2w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 2w + 11 + w2 = 0 + 11

Reorder the terms:
-11 + 11 + 2w + w2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 2w + w2 = 0 + 11
2w + w2 = 0 + 11

Combine like terms: 0 + 11 = 11
2w + w2 = 11

The w term is 2w.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2w + 1 + w2 = 11 + 1

Reorder the terms:
1 + 2w + w2 = 11 + 1

Combine like terms: 11 + 1 = 12
1 + 2w + w2 = 12

Factor a perfect square on the left side:
(w + 1)(w + 1) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(w + 1) equal to 3.464101615 and -3.464101615.

Subproblem 1
w + 1 = 3.464101615

Simplifying
w + 1 = 3.464101615

Reorder the terms:
1 + w = 3.464101615

Solving
1 + w = 3.464101615

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = 3.464101615 + -1

Combine like terms: 1 + -1 = 0
0 + w = 3.464101615 + -1
w = 3.464101615 + -1

Combine like terms: 3.464101615 + -1 = 2.464101615
w = 2.464101615

Simplifying
w = 2.464101615

Subproblem 2
w + 1 = -3.464101615

Simplifying
w + 1 = -3.464101615

Reorder the terms:
1 + w = -3.464101615

Solving
1 + w = -3.464101615

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = -3.464101615 + -1

Combine like terms: 1 + -1 = 0
0 + w = -3.464101615 + -1
w = -3.464101615 + -1

Combine like terms: -3.464101615 + -1 = -4.464101615
w = -4.464101615

Simplifying
w = -4.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.464101615, -4.464101615}