5w^2+112w-228=0

Solution for 5w^2+112w-228=0 equation:

Simplifying
5w2 + 112w + -228 = 0

Reorder the terms:
-228 + 112w + 5w2 = 0

Solving
-228 + 112w + 5w2 = 0

Solving for variable 'w'.

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

Divide each side by '5'.
-45.6 + 22.4w + w2 = 0

Move the constant term to the right:

Add '45.6' to each side of the equation.
-45.6 + 22.4w + 45.6 + w2 = 0 + 45.6

Reorder the terms:
-45.6 + 45.6 + 22.4w + w2 = 0 + 45.6

Combine like terms: -45.6 + 45.6 = 0.0
0.0 + 22.4w + w2 = 0 + 45.6
22.4w + w2 = 0 + 45.6

Combine like terms: 0 + 45.6 = 45.6
22.4w + w2 = 45.6

The w term is 22.4w.  Take half its coefficient (11.2).
Square it (125.44) and add it to both sides.

Add '125.44' to each side of the equation.
22.4w + 125.44 + w2 = 45.6 + 125.44

Reorder the terms:
125.44 + 22.4w + w2 = 45.6 + 125.44

Combine like terms: 45.6 + 125.44 = 171.04
125.44 + 22.4w + w2 = 171.04

Factor a perfect square on the left side:
(w + 11.2)(w + 11.2) = 171.04

Calculate the square root of the right side: 13.078226179

Break this problem into two subproblems by setting 
(w + 11.2) equal to 13.078226179 and -13.078226179.

Subproblem 1
w + 11.2 = 13.078226179

Simplifying
w + 11.2 = 13.078226179

Reorder the terms:
11.2 + w = 13.078226179

Solving
11.2 + w = 13.078226179

Solving for variable 'w'.

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

Add '-11.2' to each side of the equation.
11.2 + -11.2 + w = 13.078226179 + -11.2

Combine like terms: 11.2 + -11.2 = 0.0
0.0 + w = 13.078226179 + -11.2
w = 13.078226179 + -11.2

Combine like terms: 13.078226179 + -11.2 = 1.878226179
w = 1.878226179

Simplifying
w = 1.878226179

Subproblem 2
w + 11.2 = -13.078226179

Simplifying
w + 11.2 = -13.078226179

Reorder the terms:
11.2 + w = -13.078226179

Solving
11.2 + w = -13.078226179

Solving for variable 'w'.

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

Add '-11.2' to each side of the equation.
11.2 + -11.2 + w = -13.078226179 + -11.2

Combine like terms: 11.2 + -11.2 = 0.0
0.0 + w = -13.078226179 + -11.2
w = -13.078226179 + -11.2

Combine like terms: -13.078226179 + -11.2 = -24.278226179
w = -24.278226179

Simplifying
w = -24.278226179

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.878226179, -24.278226179}