-32x^2+3025x+665500=0

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Solution for -32x^2+3025x+665500=0 equation: 


Simplifying
-32x2 + 3025x + 665500 = 0

Reorder the terms:
665500 + 3025x + -32x2 = 0

Solving
665500 + 3025x + -32x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-32 the coefficient of the squared term: 

Divide each side by '-32'.
-20796.875 + -94.53125x + x2 = 0

Move the constant term to the right:

Add '20796.875' to each side of the equation.
-20796.875 + -94.53125x + 20796.875 + x2 = 0 + 20796.875

Reorder the terms:
-20796.875 + 20796.875 + -94.53125x + x2 = 0 + 20796.875

Combine like terms: -20796.875 + 20796.875 = 0.000
0.000 + -94.53125x + x2 = 0 + 20796.875
-94.53125x + x2 = 0 + 20796.875

Combine like terms: 0 + 20796.875 = 20796.875
-94.53125x + x2 = 20796.875

The x term is -94.53125x.  Take half its coefficient (-47.265625).
Square it (2234.039307) and add it to both sides.

Add '2234.039307' to each side of the equation.
-94.53125x + 2234.039307 + x2 = 20796.875 + 2234.039307

Reorder the terms:
2234.039307 + -94.53125x + x2 = 20796.875 + 2234.039307

Combine like terms: 20796.875 + 2234.039307 = 23030.914307
2234.039307 + -94.53125x + x2 = 23030.914307

Factor a perfect square on the left side:
(x + -47.265625)(x + -47.265625) = 23030.914307

Calculate the square root of the right side: 151.759396108

Break this problem into two subproblems by setting 
(x + -47.265625) equal to 151.759396108 and -151.759396108.


Subproblem 1
x + -47.265625 = 151.759396108

Simplifying
x + -47.265625 = 151.759396108

Reorder the terms:
-47.265625 + x = 151.759396108

Solving
-47.265625 + x = 151.759396108

Solving for variable 'x'.

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

Add '47.265625' to each side of the equation.
-47.265625 + 47.265625 + x = 151.759396108 + 47.265625

Combine like terms: -47.265625 + 47.265625 = 0.000000
0.000000 + x = 151.759396108 + 47.265625
x = 151.759396108 + 47.265625

Combine like terms: 151.759396108 + 47.265625 = 199.025021108
x = 199.025021108

Simplifying
x = 199.025021108


Subproblem 2
x + -47.265625 = -151.759396108

Simplifying
x + -47.265625 = -151.759396108

Reorder the terms:
-47.265625 + x = -151.759396108

Solving
-47.265625 + x = -151.759396108

Solving for variable 'x'.

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

Add '47.265625' to each side of the equation.
-47.265625 + 47.265625 + x = -151.759396108 + 47.265625

Combine like terms: -47.265625 + 47.265625 = 0.000000
0.000000 + x = -151.759396108 + 47.265625
x = -151.759396108 + 47.265625

Combine like terms: -151.759396108 + 47.265625 = -104.493771108
x = -104.493771108

Simplifying
x = -104.493771108


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {199.025021108, -104.493771108}

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