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 = 2.6875
1.5625 + -2.5x + x2 = 2.6875

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 2.6875

Calculate the square root of the right side: 1.639359631

Break this problem into two subproblems by setting 
(x + -1.25) equal to 1.639359631 and -1.639359631.


Subproblem 1
x + -1.25 = 1.639359631

Simplifying
x + -1.25 = 1.639359631

Reorder the terms:
-1.25 + x = 1.639359631

Solving
-1.25 + x = 1.639359631

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 = 1.639359631 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 1.639359631 + 1.25
x = 1.639359631 + 1.25

Combine like terms: 1.639359631 + 1.25 = 2.889359631
x = 2.889359631

Simplifying
x = 2.889359631


Subproblem 2
x + -1.25 = -1.639359631

Simplifying
x + -1.25 = -1.639359631

Reorder the terms:
-1.25 + x = -1.639359631

Solving
-1.25 + x = -1.639359631

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 = -1.639359631 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -1.639359631 + 1.25
x = -1.639359631 + 1.25

Combine like terms: -1.639359631 + 1.25 = -0.389359631
x = -0.389359631

Simplifying
x = -0.389359631


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.889359631, -0.389359631}

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