-32x^2+22500x-80=0

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Solution for -32x^2+22500x-80=0 equation: 


Simplifying
-32x2 + 22500x + -80 = 0

Reorder the terms:
-80 + 22500x + -32x2 = 0

Solving
-80 + 22500x + -32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-20 + 5625x + -8x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-20 + 5625x + -8x2)' equal to zero and attempt to solve:

Simplifying
-20 + 5625x + -8x2 = 0

Solving
-20 + 5625x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
2.5 + -703.125x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -703.125x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -703.125x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -703.125x + x2 = 0 + -2.5
-703.125x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-703.125x + x2 = -2.5

The x term is -703.125x.  Take half its coefficient (-351.5625).
Square it (123596.1914) and add it to both sides.

Add '123596.1914' to each side of the equation.
-703.125x + 123596.1914 + x2 = -2.5 + 123596.1914

Reorder the terms:
123596.1914 + -703.125x + x2 = -2.5 + 123596.1914

Combine like terms: -2.5 + 123596.1914 = 123593.6914
123596.1914 + -703.125x + x2 = 123593.6914

Factor a perfect square on the left side:
(x + -351.5625)(x + -351.5625) = 123593.6914

Calculate the square root of the right side: 351.558944418

Break this problem into two subproblems by setting 
(x + -351.5625) equal to 351.558944418 and -351.558944418.


Subproblem 1
x + -351.5625 = 351.558944418

Simplifying
x + -351.5625 = 351.558944418

Reorder the terms:
-351.5625 + x = 351.558944418

Solving
-351.5625 + x = 351.558944418

Solving for variable 'x'.

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

Add '351.5625' to each side of the equation.
-351.5625 + 351.5625 + x = 351.558944418 + 351.5625

Combine like terms: -351.5625 + 351.5625 = 0.0000
0.0000 + x = 351.558944418 + 351.5625
x = 351.558944418 + 351.5625

Combine like terms: 351.558944418 + 351.5625 = 703.121444418
x = 703.121444418

Simplifying
x = 703.121444418


Subproblem 2
x + -351.5625 = -351.558944418

Simplifying
x + -351.5625 = -351.558944418

Reorder the terms:
-351.5625 + x = -351.558944418

Solving
-351.5625 + x = -351.558944418

Solving for variable 'x'.

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

Add '351.5625' to each side of the equation.
-351.5625 + 351.5625 + x = -351.558944418 + 351.5625

Combine like terms: -351.5625 + 351.5625 = 0.0000
0.0000 + x = -351.558944418 + 351.5625
x = -351.558944418 + 351.5625

Combine like terms: -351.558944418 + 351.5625 = 0.003555582
x = 0.003555582

Simplifying
x = 0.003555582


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {703.121444418, 0.003555582}
Solution
x = {703.121444418, 0.003555582}

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