-0.25*x^2+1.25*x-1=0

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Solution for -0.25*x^2+1.25*x-1=0 equation: 


Simplifying
-0.25x2 + 1.25x + -1 = 0

Reorder the terms:
-1 + 1.25x + -0.25x2 = 0

Solving
-1 + 1.25x + -0.25x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
4 + -5x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -5x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -5x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x + x2 = 0 + -4
-5x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5x + x2 = -4

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -4 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -4 + 6.25

Combine like terms: -4 + 6.25 = 2.25
6.25 + -5x + x2 = 2.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 2.25

Calculate the square root of the right side: 1.5

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.5 and -1.5.


Subproblem 1
x + -2.5 = 1.5

Simplifying
x + -2.5 = 1.5

Reorder the terms:
-2.5 + x = 1.5

Solving
-2.5 + x = 1.5

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.5 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.5 + 2.5
x = 1.5 + 2.5

Combine like terms: 1.5 + 2.5 = 4
x = 4

Simplifying
x = 4


Subproblem 2
x + -2.5 = -1.5

Simplifying
x + -2.5 = -1.5

Reorder the terms:
-2.5 + x = -1.5

Solving
-2.5 + x = -1.5

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.5 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.5 + 2.5
x = -1.5 + 2.5

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

Simplifying
x = 1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4, 1}

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