w^2+12w+36=2w^2-17w+30

Solution for w^2+12w+36=2w^2-17w+30 equation:

Simplifying
w2 + 12w + 36 = 2w2 + -17w + 30

Reorder the terms:
36 + 12w + w2 = 2w2 + -17w + 30

Reorder the terms:
36 + 12w + w2 = 30 + -17w + 2w2

Solving
36 + 12w + w2 = 30 + -17w + 2w2

Solving for variable 'w'.

Reorder the terms:
36 + -30 + 12w + 17w + w2 + -2w2 = 30 + -17w + 2w2 + -30 + 17w + -2w2

Combine like terms: 36 + -30 = 6
6 + 12w + 17w + w2 + -2w2 = 30 + -17w + 2w2 + -30 + 17w + -2w2

Combine like terms: 12w + 17w = 29w
6 + 29w + w2 + -2w2 = 30 + -17w + 2w2 + -30 + 17w + -2w2

Combine like terms: w2 + -2w2 = -1w2
6 + 29w + -1w2 = 30 + -17w + 2w2 + -30 + 17w + -2w2

Reorder the terms:
6 + 29w + -1w2 = 30 + -30 + -17w + 17w + 2w2 + -2w2

Combine like terms: 30 + -30 = 0
6 + 29w + -1w2 = 0 + -17w + 17w + 2w2 + -2w2
6 + 29w + -1w2 = -17w + 17w + 2w2 + -2w2

Combine like terms: -17w + 17w = 0
6 + 29w + -1w2 = 0 + 2w2 + -2w2
6 + 29w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
6 + 29w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + -29w + w2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -29w + 6 + w2 = 0 + 6

Reorder the terms:
-6 + 6 + -29w + w2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -29w + w2 = 0 + 6
-29w + w2 = 0 + 6

Combine like terms: 0 + 6 = 6
-29w + w2 = 6

The w term is -29w.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29w + 210.25 + w2 = 6 + 210.25

Reorder the terms:
210.25 + -29w + w2 = 6 + 210.25

Combine like terms: 6 + 210.25 = 216.25
210.25 + -29w + w2 = 216.25

Factor a perfect square on the left side:
(w + -14.5)(w + -14.5) = 216.25

Calculate the square root of the right side: 14.70544117

Break this problem into two subproblems by setting 
(w + -14.5) equal to 14.70544117 and -14.70544117.

Subproblem 1
w + -14.5 = 14.70544117

Simplifying
w + -14.5 = 14.70544117

Reorder the terms:
-14.5 + w = 14.70544117

Solving
-14.5 + w = 14.70544117

Solving for variable 'w'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + w = 14.70544117 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + w = 14.70544117 + 14.5
w = 14.70544117 + 14.5

Combine like terms: 14.70544117 + 14.5 = 29.20544117
w = 29.20544117

Simplifying
w = 29.20544117

Subproblem 2
w + -14.5 = -14.70544117

Simplifying
w + -14.5 = -14.70544117

Reorder the terms:
-14.5 + w = -14.70544117

Solving
-14.5 + w = -14.70544117

Solving for variable 'w'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + w = -14.70544117 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + w = -14.70544117 + 14.5
w = -14.70544117 + 14.5

Combine like terms: -14.70544117 + 14.5 = -0.20544117
w = -0.20544117

Simplifying
w = -0.20544117

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {29.20544117, -0.20544117}