-32x^2+22500x-2025000=0

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Solution for -32x^2+22500x-2025000=0 equation: 


Simplifying
-32x2 + 22500x + -2025000 = 0

Reorder the terms:
-2025000 + 22500x + -32x2 = 0

Solving
-2025000 + 22500x + -32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-506250 + 5625x + -8x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-506250 + 5625x + -8x2)' equal to zero and attempt to solve:

Simplifying
-506250 + 5625x + -8x2 = 0

Solving
-506250 + 5625x + -8x2 = 0

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

Divide each side by '-8'.
63281.25 + -703.125x + x2 = 0

Move the constant term to the right:

Add '-63281.25' to each side of the equation.
63281.25 + -703.125x + -63281.25 + x2 = 0 + -63281.25

Reorder the terms:
63281.25 + -63281.25 + -703.125x + x2 = 0 + -63281.25

Combine like terms: 63281.25 + -63281.25 = 0.00
0.00 + -703.125x + x2 = 0 + -63281.25
-703.125x + x2 = 0 + -63281.25

Combine like terms: 0 + -63281.25 = -63281.25
-703.125x + x2 = -63281.25

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 = -63281.25 + 123596.1914

Reorder the terms:
123596.1914 + -703.125x + x2 = -63281.25 + 123596.1914

Combine like terms: -63281.25 + 123596.1914 = 60314.9414
123596.1914 + -703.125x + x2 = 60314.9414

Factor a perfect square on the left side:
(x + -351.5625)(x + -351.5625) = 60314.9414

Calculate the square root of the right side: 245.591004314

Break this problem into two subproblems by setting 
(x + -351.5625) equal to 245.591004314 and -245.591004314.


Subproblem 1
x + -351.5625 = 245.591004314

Simplifying
x + -351.5625 = 245.591004314

Reorder the terms:
-351.5625 + x = 245.591004314

Solving
-351.5625 + x = 245.591004314

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 = 245.591004314 + 351.5625

Combine like terms: -351.5625 + 351.5625 = 0.0000
0.0000 + x = 245.591004314 + 351.5625
x = 245.591004314 + 351.5625

Combine like terms: 245.591004314 + 351.5625 = 597.153504314
x = 597.153504314

Simplifying
x = 597.153504314


Subproblem 2
x + -351.5625 = -245.591004314

Simplifying
x + -351.5625 = -245.591004314

Reorder the terms:
-351.5625 + x = -245.591004314

Solving
-351.5625 + x = -245.591004314

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 = -245.591004314 + 351.5625

Combine like terms: -351.5625 + 351.5625 = 0.0000
0.0000 + x = -245.591004314 + 351.5625
x = -245.591004314 + 351.5625

Combine like terms: -245.591004314 + 351.5625 = 105.971495686
x = 105.971495686

Simplifying
x = 105.971495686


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {597.153504314, 105.971495686}
Solution
x = {597.153504314, 105.971495686}

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