0=-0.125x^2+1.125x+1.25

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Solution for 0=-0.125x^2+1.125x+1.25 equation: 


Simplifying
0 = -0.125x2 + 1.125x + 1.25

Reorder the terms:
0 = 1.25 + 1.125x + -0.125x2

Solving
0 = 1.25 + 1.125x + -0.125x2

Solving for variable 'x'.

Combine like terms: 0 + -1.25 = -1.25
-1.25 + -1.125x + 0.125x2 = 1.25 + 1.125x + -0.125x2 + -1.25 + -1.125x + 0.125x2

Reorder the terms:
-1.25 + -1.125x + 0.125x2 = 1.25 + -1.25 + 1.125x + -1.125x + -0.125x2 + 0.125x2

Combine like terms: 1.25 + -1.25 = 0.00
-1.25 + -1.125x + 0.125x2 = 0.00 + 1.125x + -1.125x + -0.125x2 + 0.125x2
-1.25 + -1.125x + 0.125x2 = 1.125x + -1.125x + -0.125x2 + 0.125x2

Combine like terms: 1.125x + -1.125x = 0.000
-1.25 + -1.125x + 0.125x2 = 0.000 + -0.125x2 + 0.125x2
-1.25 + -1.125x + 0.125x2 = -0.125x2 + 0.125x2

Combine like terms: -0.125x2 + 0.125x2 = 0.000
-1.25 + -1.125x + 0.125x2 = 0.000

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

Divide each side by '0.125'.
-10 + -9x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -9x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -9x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -9x + x2 = 0 + 10
-9x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-9x + x2 = 10

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 10 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 10 + 20.25

Combine like terms: 10 + 20.25 = 30.25
20.25 + -9x + x2 = 30.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 30.25

Calculate the square root of the right side: 5.5

Break this problem into two subproblems by setting 
(x + -4.5) equal to 5.5 and -5.5.


Subproblem 1
x + -4.5 = 5.5

Simplifying
x + -4.5 = 5.5

Reorder the terms:
-4.5 + x = 5.5

Solving
-4.5 + x = 5.5

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 5.5 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 5.5 + 4.5
x = 5.5 + 4.5

Combine like terms: 5.5 + 4.5 = 10
x = 10

Simplifying
x = 10


Subproblem 2
x + -4.5 = -5.5

Simplifying
x + -4.5 = -5.5

Reorder the terms:
-4.5 + x = -5.5

Solving
-4.5 + x = -5.5

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -5.5 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -5.5 + 4.5
x = -5.5 + 4.5

Combine like terms: -5.5 + 4.5 = -1
x = -1

Simplifying
x = -1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10, -1}

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