0=2w^2+5w-300

Solution for 0=2w^2+5w-300 equation:

Simplifying
0 = 2w2 + 5w + -300

Reorder the terms:
0 = -300 + 5w + 2w2

Solving
0 = -300 + 5w + 2w2

Solving for variable 'w'.

Combine like terms: 0 + 300 = 300
300 + -5w + -2w2 = -300 + 5w + 2w2 + 300 + -5w + -2w2

Reorder the terms:
300 + -5w + -2w2 = -300 + 300 + 5w + -5w + 2w2 + -2w2

Combine like terms: -300 + 300 = 0
300 + -5w + -2w2 = 0 + 5w + -5w + 2w2 + -2w2
300 + -5w + -2w2 = 5w + -5w + 2w2 + -2w2

Combine like terms: 5w + -5w = 0
300 + -5w + -2w2 = 0 + 2w2 + -2w2
300 + -5w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
300 + -5w + -2w2 = 0

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

Divide each side by '-2'.
-150 + 2.5w + w2 = 0

Move the constant term to the right:

Add '150' to each side of the equation.
-150 + 2.5w + 150 + w2 = 0 + 150

Reorder the terms:
-150 + 150 + 2.5w + w2 = 0 + 150

Combine like terms: -150 + 150 = 0
0 + 2.5w + w2 = 0 + 150
2.5w + w2 = 0 + 150

Combine like terms: 0 + 150 = 150
2.5w + w2 = 150

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 = 150 + 1.5625

Reorder the terms:
1.5625 + 2.5w + w2 = 150 + 1.5625

Combine like terms: 150 + 1.5625 = 151.5625
1.5625 + 2.5w + w2 = 151.5625

Factor a perfect square on the left side:
(w + 1.25)(w + 1.25) = 151.5625

Calculate the square root of the right side: 12.311072252

Break this problem into two subproblems by setting 
(w + 1.25) equal to 12.311072252 and -12.311072252.

Subproblem 1
w + 1.25 = 12.311072252

Simplifying
w + 1.25 = 12.311072252

Reorder the terms:
1.25 + w = 12.311072252

Solving
1.25 + w = 12.311072252

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 = 12.311072252 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + w = 12.311072252 + -1.25
w = 12.311072252 + -1.25

Combine like terms: 12.311072252 + -1.25 = 11.061072252
w = 11.061072252

Simplifying
w = 11.061072252

Subproblem 2
w + 1.25 = -12.311072252

Simplifying
w + 1.25 = -12.311072252

Reorder the terms:
1.25 + w = -12.311072252

Solving
1.25 + w = -12.311072252

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 = -12.311072252 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + w = -12.311072252 + -1.25
w = -12.311072252 + -1.25

Combine like terms: -12.311072252 + -1.25 = -13.561072252
w = -13.561072252

Simplifying
w = -13.561072252

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {11.061072252, -13.561072252}