128.25=-x^2+23x

Solution for 128.25=-x^2+23x equation:

Simplifying
128.25 = -1x2 + 23x

Reorder the terms:
128.25 = 23x + -1x2

Solving
128.25 = 23x + -1x2

Solving for variable 'x'.

Reorder the terms:
128.25 + -23x + x2 = 23x + -23x + -1x2 + x2

Combine like terms: 23x + -23x = 0
128.25 + -23x + x2 = 0 + -1x2 + x2
128.25 + -23x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
128.25 + -23x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-128.25' to each side of the equation.
128.25 + -23x + -128.25 + x2 = 0 + -128.25

Reorder the terms:
128.25 + -128.25 + -23x + x2 = 0 + -128.25

Combine like terms: 128.25 + -128.25 = 0.00
0.00 + -23x + x2 = 0 + -128.25
-23x + x2 = 0 + -128.25

Combine like terms: 0 + -128.25 = -128.25
-23x + x2 = -128.25

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = -128.25 + 132.25

Reorder the terms:
132.25 + -23x + x2 = -128.25 + 132.25

Combine like terms: -128.25 + 132.25 = 4
132.25 + -23x + x2 = 4

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + -11.5) equal to 2 and -2.

Subproblem 1
x + -11.5 = 2

Simplifying
x + -11.5 = 2

Reorder the terms:
-11.5 + x = 2

Solving
-11.5 + x = 2

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = 2 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = 2 + 11.5
x = 2 + 11.5

Combine like terms: 2 + 11.5 = 13.5
x = 13.5

Simplifying
x = 13.5

Subproblem 2
x + -11.5 = -2

Simplifying
x + -11.5 = -2

Reorder the terms:
-11.5 + x = -2

Solving
-11.5 + x = -2

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = -2 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = -2 + 11.5
x = -2 + 11.5

Combine like terms: -2 + 11.5 = 9.5
x = 9.5

Simplifying
x = 9.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.5, 9.5}