x^2+x-2.125=0

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Solution for x^2+x-2.125=0 equation: 


Simplifying
x2 + x + -2.125 = 0

Reorder the terms:
-2.125 + x + x2 = 0

Solving
-2.125 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.125' to each side of the equation.
-2.125 + x + 2.125 + x2 = 0 + 2.125

Reorder the terms:
-2.125 + 2.125 + x + x2 = 0 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x + x2 = 0 + 2.125
x + x2 = 0 + 2.125

Combine like terms: 0 + 2.125 = 2.125
x + x2 = 2.125

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 2.125 + 0.25

Reorder the terms:
0.25 + x + x2 = 2.125 + 0.25

Combine like terms: 2.125 + 0.25 = 2.375
0.25 + x + x2 = 2.375

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.375

Calculate the square root of the right side: 1.541103501

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.541103501 and -1.541103501.


Subproblem 1
x + 0.5 = 1.541103501

Simplifying
x + 0.5 = 1.541103501

Reorder the terms:
0.5 + x = 1.541103501

Solving
0.5 + x = 1.541103501

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.541103501 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.541103501 + -0.5
x = 1.541103501 + -0.5

Combine like terms: 1.541103501 + -0.5 = 1.041103501
x = 1.041103501

Simplifying
x = 1.041103501


Subproblem 2
x + 0.5 = -1.541103501

Simplifying
x + 0.5 = -1.541103501

Reorder the terms:
0.5 + x = -1.541103501

Solving
0.5 + x = -1.541103501

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.541103501 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.541103501 + -0.5
x = -1.541103501 + -0.5

Combine like terms: -1.541103501 + -0.5 = -2.041103501
x = -2.041103501

Simplifying
x = -2.041103501


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.041103501, -2.041103501}

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