-16x^2+1000x-1950=0

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Solution for -16x^2+1000x-1950=0 equation: 


Simplifying
-16x2 + 1000x + -1950 = 0

Reorder the terms:
-1950 + 1000x + -16x2 = 0

Solving
-1950 + 1000x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-975 + 500x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-975 + 500x + -8x2)' equal to zero and attempt to solve:

Simplifying
-975 + 500x + -8x2 = 0

Solving
-975 + 500x + -8x2 = 0

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

Divide each side by '-8'.
121.875 + -62.5x + x2 = 0

Move the constant term to the right:

Add '-121.875' to each side of the equation.
121.875 + -62.5x + -121.875 + x2 = 0 + -121.875

Reorder the terms:
121.875 + -121.875 + -62.5x + x2 = 0 + -121.875

Combine like terms: 121.875 + -121.875 = 0.000
0.000 + -62.5x + x2 = 0 + -121.875
-62.5x + x2 = 0 + -121.875

Combine like terms: 0 + -121.875 = -121.875
-62.5x + x2 = -121.875

The x term is -62.5x.  Take half its coefficient (-31.25).
Square it (976.5625) and add it to both sides.

Add '976.5625' to each side of the equation.
-62.5x + 976.5625 + x2 = -121.875 + 976.5625

Reorder the terms:
976.5625 + -62.5x + x2 = -121.875 + 976.5625

Combine like terms: -121.875 + 976.5625 = 854.6875
976.5625 + -62.5x + x2 = 854.6875

Factor a perfect square on the left side:
(x + -31.25)(x + -31.25) = 854.6875

Calculate the square root of the right side: 29.235038909

Break this problem into two subproblems by setting 
(x + -31.25) equal to 29.235038909 and -29.235038909.


Subproblem 1
x + -31.25 = 29.235038909

Simplifying
x + -31.25 = 29.235038909

Reorder the terms:
-31.25 + x = 29.235038909

Solving
-31.25 + x = 29.235038909

Solving for variable 'x'.

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

Add '31.25' to each side of the equation.
-31.25 + 31.25 + x = 29.235038909 + 31.25

Combine like terms: -31.25 + 31.25 = 0.00
0.00 + x = 29.235038909 + 31.25
x = 29.235038909 + 31.25

Combine like terms: 29.235038909 + 31.25 = 60.485038909
x = 60.485038909

Simplifying
x = 60.485038909


Subproblem 2
x + -31.25 = -29.235038909

Simplifying
x + -31.25 = -29.235038909

Reorder the terms:
-31.25 + x = -29.235038909

Solving
-31.25 + x = -29.235038909

Solving for variable 'x'.

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

Add '31.25' to each side of the equation.
-31.25 + 31.25 + x = -29.235038909 + 31.25

Combine like terms: -31.25 + 31.25 = 0.00
0.00 + x = -29.235038909 + 31.25
x = -29.235038909 + 31.25

Combine like terms: -29.235038909 + 31.25 = 2.014961091
x = 2.014961091

Simplifying
x = 2.014961091


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {60.485038909, 2.014961091}
Solution
x = {60.485038909, 2.014961091}

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