231=-.56y^2+31.74y+117.22

Solution for 231=-.56y^2+31.74y+117.22 equation:

Simplifying
231 = -0.56y2 + 31.74y + 117.22

Reorder the terms:
231 = 117.22 + 31.74y + -0.56y2

Solving
231 = 117.22 + 31.74y + -0.56y2

Solving for variable 'y'.

Combine like terms: 231 + -117.22 = 113.78
113.78 + -31.74y + 0.56y2 = 117.22 + 31.74y + -0.56y2 + -117.22 + -31.74y + 0.56y2

Reorder the terms:
113.78 + -31.74y + 0.56y2 = 117.22 + -117.22 + 31.74y + -31.74y + -0.56y2 + 0.56y2

Combine like terms: 117.22 + -117.22 = 0.00
113.78 + -31.74y + 0.56y2 = 0.00 + 31.74y + -31.74y + -0.56y2 + 0.56y2
113.78 + -31.74y + 0.56y2 = 31.74y + -31.74y + -0.56y2 + 0.56y2

Combine like terms: 31.74y + -31.74y = 0.00
113.78 + -31.74y + 0.56y2 = 0.00 + -0.56y2 + 0.56y2
113.78 + -31.74y + 0.56y2 = -0.56y2 + 0.56y2

Combine like terms: -0.56y2 + 0.56y2 = 0.00
113.78 + -31.74y + 0.56y2 = 0.00

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

Divide each side by '0.56'.
203.1785714 + -56.67857143y + y2 = 0

Move the constant term to the right:

Add '-203.1785714' to each side of the equation.
203.1785714 + -56.67857143y + -203.1785714 + y2 = 0 + -203.1785714

Reorder the terms:
203.1785714 + -203.1785714 + -56.67857143y + y2 = 0 + -203.1785714

Combine like terms: 203.1785714 + -203.1785714 = 0.0000000
0.0000000 + -56.67857143y + y2 = 0 + -203.1785714
-56.67857143y + y2 = 0 + -203.1785714

Combine like terms: 0 + -203.1785714 = -203.1785714
-56.67857143y + y2 = -203.1785714

The y term is -56.67857143y.  Take half its coefficient (-28.33928572).
Square it (803.1151151) and add it to both sides.

Add '803.1151151' to each side of the equation.
-56.67857143y + 803.1151151 + y2 = -203.1785714 + 803.1151151

Reorder the terms:
803.1151151 + -56.67857143y + y2 = -203.1785714 + 803.1151151

Combine like terms: -203.1785714 + 803.1151151 = 599.9365437
803.1151151 + -56.67857143y + y2 = 599.9365437

Factor a perfect square on the left side:
(y + -28.33928572)(y + -28.33928572) = 599.9365437

Calculate the square root of the right side: 24.493602097

Break this problem into two subproblems by setting 
(y + -28.33928572) equal to 24.493602097 and -24.493602097.

Subproblem 1
y + -28.33928572 = 24.493602097

Simplifying
y + -28.33928572 = 24.493602097

Reorder the terms:
-28.33928572 + y = 24.493602097

Solving
-28.33928572 + y = 24.493602097

Solving for variable 'y'.

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

Add '28.33928572' to each side of the equation.
-28.33928572 + 28.33928572 + y = 24.493602097 + 28.33928572

Combine like terms: -28.33928572 + 28.33928572 = 0.00000000
0.00000000 + y = 24.493602097 + 28.33928572
y = 24.493602097 + 28.33928572

Combine like terms: 24.493602097 + 28.33928572 = 52.832887817
y = 52.832887817

Simplifying
y = 52.832887817

Subproblem 2
y + -28.33928572 = -24.493602097

Simplifying
y + -28.33928572 = -24.493602097

Reorder the terms:
-28.33928572 + y = -24.493602097

Solving
-28.33928572 + y = -24.493602097

Solving for variable 'y'.

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

Add '28.33928572' to each side of the equation.
-28.33928572 + 28.33928572 + y = -24.493602097 + 28.33928572

Combine like terms: -28.33928572 + 28.33928572 = 0.00000000
0.00000000 + y = -24.493602097 + 28.33928572
y = -24.493602097 + 28.33928572

Combine like terms: -24.493602097 + 28.33928572 = 3.845683623
y = 3.845683623

Simplifying
y = 3.845683623

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {52.832887817, 3.845683623}