2w^2-5w-9=0

Solution for 2w^2-5w-9=0 equation:

Simplifying
2w2 + -5w + -9 = 0

Reorder the terms:
-9 + -5w + 2w2 = 0

Solving
-9 + -5w + 2w2 = 0

Solving for variable 'w'.

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

Divide each side by '2'.
-4.5 + -2.5w + w2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -2.5w + 4.5 + w2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -2.5w + w2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -2.5w + w2 = 0 + 4.5
-2.5w + w2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-2.5w + w2 = 4.5

The w term is -2.5w.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5w + 1.5625 + w2 = 4.5 + 1.5625

Reorder the terms:
1.5625 + -2.5w + w2 = 4.5 + 1.5625

Combine like terms: 4.5 + 1.5625 = 6.0625
1.5625 + -2.5w + w2 = 6.0625

Factor a perfect square on the left side:
(w + -1.25)(w + -1.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(w + -1.25) equal to 2.46221445 and -2.46221445.

Subproblem 1
w + -1.25 = 2.46221445

Simplifying
w + -1.25 = 2.46221445

Reorder the terms:
-1.25 + w = 2.46221445

Solving
-1.25 + w = 2.46221445

Solving for variable 'w'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + w = 2.46221445 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + w = 2.46221445 + 1.25
w = 2.46221445 + 1.25

Combine like terms: 2.46221445 + 1.25 = 3.71221445
w = 3.71221445

Simplifying
w = 3.71221445

Subproblem 2
w + -1.25 = -2.46221445

Simplifying
w + -1.25 = -2.46221445

Reorder the terms:
-1.25 + w = -2.46221445

Solving
-1.25 + w = -2.46221445

Solving for variable 'w'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + w = -2.46221445 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + w = -2.46221445 + 1.25
w = -2.46221445 + 1.25

Combine like terms: -2.46221445 + 1.25 = -1.21221445
w = -1.21221445

Simplifying
w = -1.21221445

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.71221445, -1.21221445}