-16x^2+1000x+3=9

Solution for -16x^2+1000x+3=9 equation:

Simplifying
-16x2 + 1000x + 3 = 9

Reorder the terms:
3 + 1000x + -16x2 = 9

Solving
3 + 1000x + -16x2 = 9

Solving for variable 'x'.

Reorder the terms:
3 + -9 + 1000x + -16x2 = 9 + -9

Combine like terms: 3 + -9 = -6
-6 + 1000x + -16x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-6 + 1000x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 500x + -8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 500x + -8x2)' equal to zero and attempt to solve:

Simplifying
-3 + 500x + -8x2 = 0

Solving
-3 + 500x + -8x2 = 0

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

Divide each side by '-8'.
0.375 + -62.5x + x2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -62.5x + -0.375 + x2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -62.5x + x2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -62.5x + x2 = 0 + -0.375
-62.5x + x2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-62.5x + x2 = -0.375

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 = -0.375 + 976.5625

Reorder the terms:
976.5625 + -62.5x + x2 = -0.375 + 976.5625

Combine like terms: -0.375 + 976.5625 = 976.1875
976.5625 + -62.5x + x2 = 976.1875

Factor a perfect square on the left side:
(x + -31.25)(x + -31.25) = 976.1875

Calculate the square root of the right side: 31.243999424

Break this problem into two subproblems by setting 
(x + -31.25) equal to 31.243999424 and -31.243999424.

Subproblem 1
x + -31.25 = 31.243999424

Simplifying
x + -31.25 = 31.243999424

Reorder the terms:
-31.25 + x = 31.243999424

Solving
-31.25 + x = 31.243999424

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 = 31.243999424 + 31.25

Combine like terms: -31.25 + 31.25 = 0.00
0.00 + x = 31.243999424 + 31.25
x = 31.243999424 + 31.25

Combine like terms: 31.243999424 + 31.25 = 62.493999424
x = 62.493999424

Simplifying
x = 62.493999424

Subproblem 2
x + -31.25 = -31.243999424

Simplifying
x + -31.25 = -31.243999424

Reorder the terms:
-31.25 + x = -31.243999424

Solving
-31.25 + x = -31.243999424

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 = -31.243999424 + 31.25

Combine like terms: -31.25 + 31.25 = 0.00
0.00 + x = -31.243999424 + 31.25
x = -31.243999424 + 31.25

Combine like terms: -31.243999424 + 31.25 = 0.006000576
x = 0.006000576

Simplifying
x = 0.006000576

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {62.493999424, 0.006000576}
Solution
x = {62.493999424, 0.006000576}