x^2-3x=-1.25

Solution for x^2-3x=-1.25 equation:

Simplifying
x2 + -3x = -1.25

Reorder the terms:
-3x + x2 = -1.25

Solving
-3x + x2 = -1.25

Solving for variable 'x'.

Reorder the terms:
1.25 + -3x + x2 = -1.25 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
1.25 + -3x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -3x + -1.25 + x2 = 0.00 + -1.25

Reorder the terms:
1.25 + -1.25 + -3x + x2 = 0.00 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -3x + x2 = 0.00 + -1.25
-3x + x2 = 0.00 + -1.25

Combine like terms: 0.00 + -1.25 = -1.25
-3x + x2 = -1.25

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -1.25 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -1.25 + 2.25

Combine like terms: -1.25 + 2.25 = 1
2.25 + -3x + x2 = 1

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1 and -1.

Subproblem 1
x + -1.5 = 1

Simplifying
x + -1.5 = 1

Reorder the terms:
-1.5 + x = 1

Solving
-1.5 + x = 1

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 1 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1 + 1.5
x = 1 + 1.5

Combine like terms: 1 + 1.5 = 2.5
x = 2.5

Simplifying
x = 2.5

Subproblem 2
x + -1.5 = -1

Simplifying
x + -1.5 = -1

Reorder the terms:
-1.5 + x = -1

Solving
-1.5 + x = -1

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -1 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1 + 1.5
x = -1 + 1.5

Combine like terms: -1 + 1.5 = 0.5
x = 0.5

Simplifying
x = 0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.5, 0.5}