x^2-1.25x+0.390625=0.130209

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Solution for x^2-1.25x+0.390625=0.130209 equation: 


Simplifying
x2 + -1.25x + 0.390625 = 0.130209

Reorder the terms:
0.390625 + -1.25x + x2 = 0.130209

Solving
0.390625 + -1.25x + x2 = 0.130209

Solving for variable 'x'.

Reorder the terms:
0.390625 + -0.130209 + -1.25x + x2 = 0.130209 + -0.130209

Combine like terms: 0.390625 + -0.130209 = 0.260416
0.260416 + -1.25x + x2 = 0.130209 + -0.130209

Combine like terms: 0.130209 + -0.130209 = 0.000000
0.260416 + -1.25x + x2 = 0.000000

Begin completing the square.

Move the constant term to the right:

Add '-0.260416' to each side of the equation.
0.260416 + -1.25x + -0.260416 + x2 = 0.000000 + -0.260416

Reorder the terms:
0.260416 + -0.260416 + -1.25x + x2 = 0.000000 + -0.260416

Combine like terms: 0.260416 + -0.260416 = 0.000000
0.000000 + -1.25x + x2 = 0.000000 + -0.260416
-1.25x + x2 = 0.000000 + -0.260416

Combine like terms: 0.000000 + -0.260416 = -0.260416
-1.25x + x2 = -0.260416

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = -0.260416 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = -0.260416 + 0.390625

Combine like terms: -0.260416 + 0.390625 = 0.130209
0.390625 + -1.25x + x2 = 0.130209

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 0.130209

Calculate the square root of the right side: 0.360844842

Break this problem into two subproblems by setting 
(x + -0.625) equal to 0.360844842 and -0.360844842.


Subproblem 1
x + -0.625 = 0.360844842

Simplifying
x + -0.625 = 0.360844842

Reorder the terms:
-0.625 + x = 0.360844842

Solving
-0.625 + x = 0.360844842

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = 0.360844842 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = 0.360844842 + 0.625
x = 0.360844842 + 0.625

Combine like terms: 0.360844842 + 0.625 = 0.985844842
x = 0.985844842

Simplifying
x = 0.985844842


Subproblem 2
x + -0.625 = -0.360844842

Simplifying
x + -0.625 = -0.360844842

Reorder the terms:
-0.625 + x = -0.360844842

Solving
-0.625 + x = -0.360844842

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = -0.360844842 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = -0.360844842 + 0.625
x = -0.360844842 + 0.625

Combine like terms: -0.360844842 + 0.625 = 0.264155158
x = 0.264155158

Simplifying
x = 0.264155158


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.985844842, 0.264155158}

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