w^2+6w-3=0

Solution for w^2+6w-3=0 equation:

Simplifying
w2 + 6w + -3 = 0

Reorder the terms:
-3 + 6w + w2 = 0

Solving
-3 + 6w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 6w + 3 + w2 = 0 + 3

Reorder the terms:
-3 + 3 + 6w + w2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6w + w2 = 0 + 3
6w + w2 = 0 + 3

Combine like terms: 0 + 3 = 3
6w + w2 = 3

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 = 3 + 9

Reorder the terms:
9 + 6w + w2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + 6w + w2 = 12

Factor a perfect square on the left side:
(w + 3)(w + 3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(w + 3) equal to 3.464101615 and -3.464101615.

Subproblem 1
w + 3 = 3.464101615

Simplifying
w + 3 = 3.464101615

Reorder the terms:
3 + w = 3.464101615

Solving
3 + w = 3.464101615

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 = 3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + w = 3.464101615 + -3
w = 3.464101615 + -3

Combine like terms: 3.464101615 + -3 = 0.464101615
w = 0.464101615

Simplifying
w = 0.464101615

Subproblem 2
w + 3 = -3.464101615

Simplifying
w + 3 = -3.464101615

Reorder the terms:
3 + w = -3.464101615

Solving
3 + w = -3.464101615

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 = -3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + w = -3.464101615 + -3
w = -3.464101615 + -3

Combine like terms: -3.464101615 + -3 = -6.464101615
w = -6.464101615

Simplifying
w = -6.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.464101615, -6.464101615}