-16x^2+500x-2990=0

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Solution for -16x^2+500x-2990=0 equation: 


Simplifying
-16x2 + 500x + -2990 = 0

Reorder the terms:
-2990 + 500x + -16x2 = 0

Solving
-2990 + 500x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1495 + 250x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1495 + 250x + -8x2)' equal to zero and attempt to solve:

Simplifying
-1495 + 250x + -8x2 = 0

Solving
-1495 + 250x + -8x2 = 0

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

Divide each side by '-8'.
186.875 + -31.25x + x2 = 0

Move the constant term to the right:

Add '-186.875' to each side of the equation.
186.875 + -31.25x + -186.875 + x2 = 0 + -186.875

Reorder the terms:
186.875 + -186.875 + -31.25x + x2 = 0 + -186.875

Combine like terms: 186.875 + -186.875 = 0.000
0.000 + -31.25x + x2 = 0 + -186.875
-31.25x + x2 = 0 + -186.875

Combine like terms: 0 + -186.875 = -186.875
-31.25x + x2 = -186.875

The x term is -31.25x.  Take half its coefficient (-15.625).
Square it (244.140625) and add it to both sides.

Add '244.140625' to each side of the equation.
-31.25x + 244.140625 + x2 = -186.875 + 244.140625

Reorder the terms:
244.140625 + -31.25x + x2 = -186.875 + 244.140625

Combine like terms: -186.875 + 244.140625 = 57.265625
244.140625 + -31.25x + x2 = 57.265625

Factor a perfect square on the left side:
(x + -15.625)(x + -15.625) = 57.265625

Calculate the square root of the right side: 7.567405434

Break this problem into two subproblems by setting 
(x + -15.625) equal to 7.567405434 and -7.567405434.


Subproblem 1
x + -15.625 = 7.567405434

Simplifying
x + -15.625 = 7.567405434

Reorder the terms:
-15.625 + x = 7.567405434

Solving
-15.625 + x = 7.567405434

Solving for variable 'x'.

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

Add '15.625' to each side of the equation.
-15.625 + 15.625 + x = 7.567405434 + 15.625

Combine like terms: -15.625 + 15.625 = 0.000
0.000 + x = 7.567405434 + 15.625
x = 7.567405434 + 15.625

Combine like terms: 7.567405434 + 15.625 = 23.192405434
x = 23.192405434

Simplifying
x = 23.192405434


Subproblem 2
x + -15.625 = -7.567405434

Simplifying
x + -15.625 = -7.567405434

Reorder the terms:
-15.625 + x = -7.567405434

Solving
-15.625 + x = -7.567405434

Solving for variable 'x'.

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

Add '15.625' to each side of the equation.
-15.625 + 15.625 + x = -7.567405434 + 15.625

Combine like terms: -15.625 + 15.625 = 0.000
0.000 + x = -7.567405434 + 15.625
x = -7.567405434 + 15.625

Combine like terms: -7.567405434 + 15.625 = 8.057594566
x = 8.057594566

Simplifying
x = 8.057594566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.192405434, 8.057594566}
Solution
x = {23.192405434, 8.057594566}

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