0.5x^2+1.125x=1.125

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Solution for 0.5x^2+1.125x=1.125 equation: 


Simplifying
0.5x2 + 1.125x = 1.125

Reorder the terms:
1.125x + 0.5x2 = 1.125

Solving
1.125x + 0.5x2 = 1.125

Solving for variable 'x'.

Reorder the terms:
-1.125 + 1.125x + 0.5x2 = 1.125 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
-1.125 + 1.125x + 0.5x2 = 0.000

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

Divide each side by '0.5'.
-2.25 + 2.25x + x2 = 0.00

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 2.25x + 2.25 + x2 = 0.00 + 2.25

Reorder the terms:
-2.25 + 2.25 + 2.25x + x2 = 0.00 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 2.25x + x2 = 0.00 + 2.25
2.25x + x2 = 0.00 + 2.25

Combine like terms: 0.00 + 2.25 = 2.25
2.25x + x2 = 2.25

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = 2.25 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 2.25 + 1.265625

Combine like terms: 2.25 + 1.265625 = 3.515625
1.265625 + 2.25x + x2 = 3.515625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 3.515625

Calculate the square root of the right side: 1.875

Break this problem into two subproblems by setting 
(x + 1.125) equal to 1.875 and -1.875.


Subproblem 1
x + 1.125 = 1.875

Simplifying
x + 1.125 = 1.875

Reorder the terms:
1.125 + x = 1.875

Solving
1.125 + x = 1.875

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = 1.875 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = 1.875 + -1.125
x = 1.875 + -1.125

Combine like terms: 1.875 + -1.125 = 0.75
x = 0.75

Simplifying
x = 0.75


Subproblem 2
x + 1.125 = -1.875

Simplifying
x + 1.125 = -1.875

Reorder the terms:
1.125 + x = -1.875

Solving
1.125 + x = -1.875

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = -1.875 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = -1.875 + -1.125
x = -1.875 + -1.125

Combine like terms: -1.875 + -1.125 = -3
x = -3

Simplifying
x = -3


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.75, -3}

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