x^2+x-1.10=0

Solution for x^2+x-1.10=0 equation:

Simplifying
x2 + x + -1.10 = 0

Reorder the terms:
-1.10 + x + x2 = 0

Solving
-1.10 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1.10' to each side of the equation.
-1.10 + x + 1.10 + x2 = 0 + 1.10

Reorder the terms:
-1.10 + 1.10 + x + x2 = 0 + 1.10

Combine like terms: -1.10 + 1.10 = 0.00
0.00 + x + x2 = 0 + 1.10
x + x2 = 0 + 1.10

Combine like terms: 0 + 1.10 = 1.1
x + x2 = 1.1

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 = 1.1 + 0.25

Reorder the terms:
0.25 + x + x2 = 1.1 + 0.25

Combine like terms: 1.1 + 0.25 = 1.35
0.25 + x + x2 = 1.35

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.35

Calculate the square root of the right side: 1.161895004

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.161895004 and -1.161895004.

Subproblem 1
x + 0.5 = 1.161895004

Simplifying
x + 0.5 = 1.161895004

Reorder the terms:
0.5 + x = 1.161895004

Solving
0.5 + x = 1.161895004

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 = 1.161895004 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.161895004 + -0.5
x = 1.161895004 + -0.5

Combine like terms: 1.161895004 + -0.5 = 0.661895004
x = 0.661895004

Simplifying
x = 0.661895004

Subproblem 2
x + 0.5 = -1.161895004

Simplifying
x + 0.5 = -1.161895004

Reorder the terms:
0.5 + x = -1.161895004

Solving
0.5 + x = -1.161895004

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 = -1.161895004 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.161895004 + -0.5
x = -1.161895004 + -0.5

Combine like terms: -1.161895004 + -0.5 = -1.661895004
x = -1.661895004

Simplifying
x = -1.661895004

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.661895004, -1.661895004}