-32x^2+2500x+200000=0

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Solution for -32x^2+2500x+200000=0 equation: 


Simplifying
-32x2 + 2500x + 200000 = 0

Reorder the terms:
200000 + 2500x + -32x2 = 0

Solving
200000 + 2500x + -32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(50000 + 625x + -8x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(50000 + 625x + -8x2)' equal to zero and attempt to solve:

Simplifying
50000 + 625x + -8x2 = 0

Solving
50000 + 625x + -8x2 = 0

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

Divide each side by '-8'.
-6250 + -78.125x + x2 = 0

Move the constant term to the right:

Add '6250' to each side of the equation.
-6250 + -78.125x + 6250 + x2 = 0 + 6250

Reorder the terms:
-6250 + 6250 + -78.125x + x2 = 0 + 6250

Combine like terms: -6250 + 6250 = 0
0 + -78.125x + x2 = 0 + 6250
-78.125x + x2 = 0 + 6250

Combine like terms: 0 + 6250 = 6250
-78.125x + x2 = 6250

The x term is -78.125x.  Take half its coefficient (-39.0625).
Square it (1525.878906) and add it to both sides.

Add '1525.878906' to each side of the equation.
-78.125x + 1525.878906 + x2 = 6250 + 1525.878906

Reorder the terms:
1525.878906 + -78.125x + x2 = 6250 + 1525.878906

Combine like terms: 6250 + 1525.878906 = 7775.878906
1525.878906 + -78.125x + x2 = 7775.878906

Factor a perfect square on the left side:
(x + -39.0625)(x + -39.0625) = 7775.878906

Calculate the square root of the right side: 88.180944121

Break this problem into two subproblems by setting 
(x + -39.0625) equal to 88.180944121 and -88.180944121.


Subproblem 1
x + -39.0625 = 88.180944121

Simplifying
x + -39.0625 = 88.180944121

Reorder the terms:
-39.0625 + x = 88.180944121

Solving
-39.0625 + x = 88.180944121

Solving for variable 'x'.

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

Add '39.0625' to each side of the equation.
-39.0625 + 39.0625 + x = 88.180944121 + 39.0625

Combine like terms: -39.0625 + 39.0625 = 0.0000
0.0000 + x = 88.180944121 + 39.0625
x = 88.180944121 + 39.0625

Combine like terms: 88.180944121 + 39.0625 = 127.243444121
x = 127.243444121

Simplifying
x = 127.243444121


Subproblem 2
x + -39.0625 = -88.180944121

Simplifying
x + -39.0625 = -88.180944121

Reorder the terms:
-39.0625 + x = -88.180944121

Solving
-39.0625 + x = -88.180944121

Solving for variable 'x'.

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

Add '39.0625' to each side of the equation.
-39.0625 + 39.0625 + x = -88.180944121 + 39.0625

Combine like terms: -39.0625 + 39.0625 = 0.0000
0.0000 + x = -88.180944121 + 39.0625
x = -88.180944121 + 39.0625

Combine like terms: -88.180944121 + 39.0625 = -49.118444121
x = -49.118444121

Simplifying
x = -49.118444121


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {127.243444121, -49.118444121}
Solution
x = {127.243444121, -49.118444121}

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