10000=25x^2+16x

Solution for 10000=25x^2+16x equation:

Simplifying
10000 = 25x2 + 16x

Reorder the terms:
10000 = 16x + 25x2

Solving
10000 = 16x + 25x2

Solving for variable 'x'.

Reorder the terms:
10000 + -16x + -25x2 = 16x + -16x + 25x2 + -25x2

Combine like terms: 16x + -16x = 0
10000 + -16x + -25x2 = 0 + 25x2 + -25x2
10000 + -16x + -25x2 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
10000 + -16x + -25x2 = 0

Begin completing the square.  Divide all terms by
-25 the coefficient of the squared term: 

Divide each side by '-25'.
-400 + 0.64x + x2 = 0

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + 0.64x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + 0.64x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + 0.64x + x2 = 0 + 400
0.64x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
0.64x + x2 = 400

The x term is 0.64x.  Take half its coefficient (0.32).
Square it (0.1024) and add it to both sides.

Add '0.1024' to each side of the equation.
0.64x + 0.1024 + x2 = 400 + 0.1024

Reorder the terms:
0.1024 + 0.64x + x2 = 400 + 0.1024

Combine like terms: 400 + 0.1024 = 400.1024
0.1024 + 0.64x + x2 = 400.1024

Factor a perfect square on the left side:
(x + 0.32)(x + 0.32) = 400.1024

Calculate the square root of the right side: 20.002559836

Break this problem into two subproblems by setting 
(x + 0.32) equal to 20.002559836 and -20.002559836.

Subproblem 1
x + 0.32 = 20.002559836

Simplifying
x + 0.32 = 20.002559836

Reorder the terms:
0.32 + x = 20.002559836

Solving
0.32 + x = 20.002559836

Solving for variable 'x'.

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

Add '-0.32' to each side of the equation.
0.32 + -0.32 + x = 20.002559836 + -0.32

Combine like terms: 0.32 + -0.32 = 0.00
0.00 + x = 20.002559836 + -0.32
x = 20.002559836 + -0.32

Combine like terms: 20.002559836 + -0.32 = 19.682559836
x = 19.682559836

Simplifying
x = 19.682559836

Subproblem 2
x + 0.32 = -20.002559836

Simplifying
x + 0.32 = -20.002559836

Reorder the terms:
0.32 + x = -20.002559836

Solving
0.32 + x = -20.002559836

Solving for variable 'x'.

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

Add '-0.32' to each side of the equation.
0.32 + -0.32 + x = -20.002559836 + -0.32

Combine like terms: 0.32 + -0.32 = 0.00
0.00 + x = -20.002559836 + -0.32
x = -20.002559836 + -0.32

Combine like terms: -20.002559836 + -0.32 = -20.322559836
x = -20.322559836

Simplifying
x = -20.322559836

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.682559836, -20.322559836}