36.25x^2-1.8x-0.64=0

Solution for 36.25x^2-1.8x-0.64=0 equation:

Simplifying
36.25x2 + -1.8x + -0.64 = 0

Reorder the terms:
-0.64 + -1.8x + 36.25x2 = 0

Solving
-0.64 + -1.8x + 36.25x2 = 0

Solving for variable 'x'.

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

Divide each side by '36.25'.
-0.01765517241 + -0.04965517241x + x2 = 0

Move the constant term to the right:

Add '0.01765517241' to each side of the equation.
-0.01765517241 + -0.04965517241x + 0.01765517241 + x2 = 0 + 0.01765517241

Reorder the terms:
-0.01765517241 + 0.01765517241 + -0.04965517241x + x2 = 0 + 0.01765517241

Combine like terms: -0.01765517241 + 0.01765517241 = 0.00000000000
0.00000000000 + -0.04965517241x + x2 = 0 + 0.01765517241
-0.04965517241x + x2 = 0 + 0.01765517241

Combine like terms: 0 + 0.01765517241 = 0.01765517241
-0.04965517241x + x2 = 0.01765517241

The x term is -0.04965517241x.  Take half its coefficient (-0.02482758621).
Square it (0.0006164090370) and add it to both sides.

Add '0.0006164090370' to each side of the equation.
-0.04965517241x + 0.0006164090370 + x2 = 0.01765517241 + 0.0006164090370

Reorder the terms:
0.0006164090370 + -0.04965517241x + x2 = 0.01765517241 + 0.0006164090370

Combine like terms: 0.01765517241 + 0.0006164090370 = 0.018271581447
0.0006164090370 + -0.04965517241x + x2 = 0.018271581447

Factor a perfect square on the left side:
(x + -0.02482758621)(x + -0.02482758621) = 0.018271581447

Calculate the square root of the right side: 0.135172414

Break this problem into two subproblems by setting 
(x + -0.02482758621) equal to 0.135172414 and -0.135172414.

Subproblem 1
x + -0.02482758621 = 0.135172414

Simplifying
x + -0.02482758621 = 0.135172414

Reorder the terms:
-0.02482758621 + x = 0.135172414

Solving
-0.02482758621 + x = 0.135172414

Solving for variable 'x'.

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

Add '0.02482758621' to each side of the equation.
-0.02482758621 + 0.02482758621 + x = 0.135172414 + 0.02482758621

Combine like terms: -0.02482758621 + 0.02482758621 = 0.00000000000
0.00000000000 + x = 0.135172414 + 0.02482758621
x = 0.135172414 + 0.02482758621

Combine like terms: 0.135172414 + 0.02482758621 = 0.16000000021
x = 0.16000000021

Simplifying
x = 0.16000000021

Subproblem 2
x + -0.02482758621 = -0.135172414

Simplifying
x + -0.02482758621 = -0.135172414

Reorder the terms:
-0.02482758621 + x = -0.135172414

Solving
-0.02482758621 + x = -0.135172414

Solving for variable 'x'.

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

Add '0.02482758621' to each side of the equation.
-0.02482758621 + 0.02482758621 + x = -0.135172414 + 0.02482758621

Combine like terms: -0.02482758621 + 0.02482758621 = 0.00000000000
0.00000000000 + x = -0.135172414 + 0.02482758621
x = -0.135172414 + 0.02482758621

Combine like terms: -0.135172414 + 0.02482758621 = -0.11034482779
x = -0.11034482779

Simplifying
x = -0.11034482779

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.16000000021, -0.11034482779}