1.25=x^2+x-2

Solution for 1.25=x^2+x-2 equation:

Simplifying
1.25 = x2 + x + -2

Reorder the terms:
1.25 = -2 + x + x2

Solving
1.25 = -2 + x + x2

Solving for variable 'x'.

Combine like terms: 1.25 + 2 = 3.25
3.25 + -1x + -1x2 = -2 + x + x2 + 2 + -1x + -1x2

Reorder the terms:
3.25 + -1x + -1x2 = -2 + 2 + x + -1x + x2 + -1x2

Combine like terms: -2 + 2 = 0
3.25 + -1x + -1x2 = 0 + x + -1x + x2 + -1x2
3.25 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
3.25 + -1x + -1x2 = 0 + x2 + -1x2
3.25 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3.25 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3.25 + x + x2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + x + 3.25 + x2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + x + x2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x + x2 = 0 + 3.25
x + x2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
x + x2 = 3.25

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.
 + 0.25 + x2 = 3.25 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 3.25 + 0.25

Combine like terms: 3.25 + 0.25 = 3.5
1.25 + x2 = 3.5

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.870828693 and -1.870828693.

Subproblem 1
x + 0.5 = 1.870828693

Simplifying
x + 0.5 = 1.870828693

Reorder the terms:
0.5 + x = 1.870828693

Solving
0.5 + x = 1.870828693

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 = 1.870828693 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.870828693 + -0.5
x = 1.870828693 + -0.5

Combine like terms: 1.870828693 + -0.5 = 1.370828693
x = 1.370828693

Simplifying
x = 1.370828693

Subproblem 2
x + 0.5 = -1.870828693

Simplifying
x + 0.5 = -1.870828693

Reorder the terms:
0.5 + x = -1.870828693

Solving
0.5 + x = -1.870828693

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 = -1.870828693 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.870828693 + -0.5
x = -1.870828693 + -0.5

Combine like terms: -1.870828693 + -0.5 = -2.370828693
x = -2.370828693

Simplifying
x = -2.370828693

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.370828693, -2.370828693}