220=(2w+5)(w-2)

Solution for 220=(2w+5)(w-2) equation:

Simplifying
220 = (2w + 5)(w + -2)

Reorder the terms:
220 = (5 + 2w)(w + -2)

Reorder the terms:
220 = (5 + 2w)(-2 + w)

Multiply (5 + 2w) * (-2 + w)
220 = (5(-2 + w) + 2w * (-2 + w))
220 = ((-2 * 5 + w * 5) + 2w * (-2 + w))
220 = ((-10 + 5w) + 2w * (-2 + w))
220 = (-10 + 5w + (-2 * 2w + w * 2w))
220 = (-10 + 5w + (-4w + 2w2))

Combine like terms: 5w + -4w = 1w
220 = (-10 + 1w + 2w2)

Solving
220 = -10 + 1w + 2w2

Solving for variable 'w'.

Combine like terms: 220 + 10 = 230
230 + -1w + -2w2 = -10 + 1w + 2w2 + 10 + -1w + -2w2

Reorder the terms:
230 + -1w + -2w2 = -10 + 10 + 1w + -1w + 2w2 + -2w2

Combine like terms: -10 + 10 = 0
230 + -1w + -2w2 = 0 + 1w + -1w + 2w2 + -2w2
230 + -1w + -2w2 = 1w + -1w + 2w2 + -2w2

Combine like terms: 1w + -1w = 0
230 + -1w + -2w2 = 0 + 2w2 + -2w2
230 + -1w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
230 + -1w + -2w2 = 0

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

Divide each side by '-2'.
-115 + 0.5w + w2 = 0

Move the constant term to the right:

Add '115' to each side of the equation.
-115 + 0.5w + 115 + w2 = 0 + 115

Reorder the terms:
-115 + 115 + 0.5w + w2 = 0 + 115

Combine like terms: -115 + 115 = 0
0 + 0.5w + w2 = 0 + 115
0.5w + w2 = 0 + 115

Combine like terms: 0 + 115 = 115
0.5w + w2 = 115

The w term is 0.5w.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5w + 0.0625 + w2 = 115 + 0.0625

Reorder the terms:
0.0625 + 0.5w + w2 = 115 + 0.0625

Combine like terms: 115 + 0.0625 = 115.0625
0.0625 + 0.5w + w2 = 115.0625

Factor a perfect square on the left side:
(w + 0.25)(w + 0.25) = 115.0625

Calculate the square root of the right side: 10.726718976

Break this problem into two subproblems by setting 
(w + 0.25) equal to 10.726718976 and -10.726718976.

Subproblem 1
w + 0.25 = 10.726718976

Simplifying
w + 0.25 = 10.726718976

Reorder the terms:
0.25 + w = 10.726718976

Solving
0.25 + w = 10.726718976

Solving for variable 'w'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + w = 10.726718976 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + w = 10.726718976 + -0.25
w = 10.726718976 + -0.25

Combine like terms: 10.726718976 + -0.25 = 10.476718976
w = 10.476718976

Simplifying
w = 10.476718976

Subproblem 2
w + 0.25 = -10.726718976

Simplifying
w + 0.25 = -10.726718976

Reorder the terms:
0.25 + w = -10.726718976

Solving
0.25 + w = -10.726718976

Solving for variable 'w'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + w = -10.726718976 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + w = -10.726718976 + -0.25
w = -10.726718976 + -0.25

Combine like terms: -10.726718976 + -0.25 = -10.976718976
w = -10.976718976

Simplifying
w = -10.976718976

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {10.476718976, -10.976718976}