x^2-2.5x+1.125=0

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Solution for x^2-2.5x+1.125=0 equation: 


Simplifying
x2 + -2.5x + 1.125 = 0

Reorder the terms:
1.125 + -2.5x + x2 = 0

Solving
1.125 + -2.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.125' to each side of the equation.
1.125 + -2.5x + -1.125 + x2 = 0 + -1.125

Reorder the terms:
1.125 + -1.125 + -2.5x + x2 = 0 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + -2.5x + x2 = 0 + -1.125
-2.5x + x2 = 0 + -1.125

Combine like terms: 0 + -1.125 = -1.125
-2.5x + x2 = -1.125

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = -1.125 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -1.125 + 1.5625

Combine like terms: -1.125 + 1.5625 = 0.4375
1.5625 + -2.5x + x2 = 0.4375

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(x + -1.25) equal to 0.661437828 and -0.661437828.


Subproblem 1
x + -1.25 = 0.661437828

Simplifying
x + -1.25 = 0.661437828

Reorder the terms:
-1.25 + x = 0.661437828

Solving
-1.25 + x = 0.661437828

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 0.661437828 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 0.661437828 + 1.25
x = 0.661437828 + 1.25

Combine like terms: 0.661437828 + 1.25 = 1.911437828
x = 1.911437828

Simplifying
x = 1.911437828


Subproblem 2
x + -1.25 = -0.661437828

Simplifying
x + -1.25 = -0.661437828

Reorder the terms:
-1.25 + x = -0.661437828

Solving
-1.25 + x = -0.661437828

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -0.661437828 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -0.661437828 + 1.25
x = -0.661437828 + 1.25

Combine like terms: -0.661437828 + 1.25 = 0.588562172
x = 0.588562172

Simplifying
x = 0.588562172


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.911437828, 0.588562172}

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