1.25x^2-2x=1

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Solution for 1.25x^2-2x=1 equation: 


Simplifying
1.25x2 + -2x = 1

Reorder the terms:
-2x + 1.25x2 = 1

Solving
-2x + 1.25x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + -2x + 1.25x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -2x + 1.25x2 = 0

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

Divide each side by '1.25'.
-0.8 + -1.6x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -1.6x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -1.6x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -1.6x + x2 = 0 + 0.8
-1.6x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-1.6x + x2 = 0.8

The x term is -1.6x.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6x + 0.64 + x2 = 0.8 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = 0.8 + 0.64

Combine like terms: 0.8 + 0.64 = 1.44
0.64 + -1.6x + x2 = 1.44

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 1.44

Calculate the square root of the right side: 1.2

Break this problem into two subproblems by setting 
(x + -0.8) equal to 1.2 and -1.2.


Subproblem 1
x + -0.8 = 1.2

Simplifying
x + -0.8 = 1.2

Reorder the terms:
-0.8 + x = 1.2

Solving
-0.8 + x = 1.2

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = 1.2 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = 1.2 + 0.8
x = 1.2 + 0.8

Combine like terms: 1.2 + 0.8 = 2
x = 2

Simplifying
x = 2


Subproblem 2
x + -0.8 = -1.2

Simplifying
x + -0.8 = -1.2

Reorder the terms:
-0.8 + x = -1.2

Solving
-0.8 + x = -1.2

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = -1.2 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = -1.2 + 0.8
x = -1.2 + 0.8

Combine like terms: -1.2 + 0.8 = -0.4
x = -0.4

Simplifying
x = -0.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2, -0.4}

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