2w^2-9w=w^2-6w+9

Solution for 2w^2-9w=w^2-6w+9 equation:

Simplifying
2w2 + -9w = w2 + -6w + 9

Reorder the terms:
-9w + 2w2 = w2 + -6w + 9

Reorder the terms:
-9w + 2w2 = 9 + -6w + w2

Solving
-9w + 2w2 = 9 + -6w + w2

Solving for variable 'w'.

Reorder the terms:
-9 + -9w + 6w + 2w2 + -1w2 = 9 + -6w + w2 + -9 + 6w + -1w2

Combine like terms: -9w + 6w = -3w
-9 + -3w + 2w2 + -1w2 = 9 + -6w + w2 + -9 + 6w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-9 + -3w + 1w2 = 9 + -6w + w2 + -9 + 6w + -1w2

Reorder the terms:
-9 + -3w + 1w2 = 9 + -9 + -6w + 6w + w2 + -1w2

Combine like terms: 9 + -9 = 0
-9 + -3w + 1w2 = 0 + -6w + 6w + w2 + -1w2
-9 + -3w + 1w2 = -6w + 6w + w2 + -1w2

Combine like terms: -6w + 6w = 0
-9 + -3w + 1w2 = 0 + w2 + -1w2
-9 + -3w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-9 + -3w + 1w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -3w + 9 + w2 = 0 + 9

Reorder the terms:
-9 + 9 + -3w + w2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -3w + w2 = 0 + 9
-3w + w2 = 0 + 9

Combine like terms: 0 + 9 = 9
-3w + w2 = 9

The w term is -3w.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3w + 2.25 + w2 = 9 + 2.25

Reorder the terms:
2.25 + -3w + w2 = 9 + 2.25

Combine like terms: 9 + 2.25 = 11.25
2.25 + -3w + w2 = 11.25

Factor a perfect square on the left side:
(w + -1.5)(w + -1.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(w + -1.5) equal to 3.354101966 and -3.354101966.

Subproblem 1
w + -1.5 = 3.354101966

Simplifying
w + -1.5 = 3.354101966

Reorder the terms:
-1.5 + w = 3.354101966

Solving
-1.5 + w = 3.354101966

Solving for variable 'w'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + w = 3.354101966 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + w = 3.354101966 + 1.5
w = 3.354101966 + 1.5

Combine like terms: 3.354101966 + 1.5 = 4.854101966
w = 4.854101966

Simplifying
w = 4.854101966

Subproblem 2
w + -1.5 = -3.354101966

Simplifying
w + -1.5 = -3.354101966

Reorder the terms:
-1.5 + w = -3.354101966

Solving
-1.5 + w = -3.354101966

Solving for variable 'w'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + w = -3.354101966 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + w = -3.354101966 + 1.5
w = -3.354101966 + 1.5

Combine like terms: -3.354101966 + 1.5 = -1.854101966
w = -1.854101966

Simplifying
w = -1.854101966

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.854101966, -1.854101966}