-16x^2+100x+2500=0

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Solution for -16x^2+100x+2500=0 equation: 


Simplifying
-16x2 + 100x + 2500 = 0

Reorder the terms:
2500 + 100x + -16x2 = 0

Solving
2500 + 100x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(625 + 25x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(625 + 25x + -4x2)' equal to zero and attempt to solve:

Simplifying
625 + 25x + -4x2 = 0

Solving
625 + 25x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-156.25 + -6.25x + x2 = 0

Move the constant term to the right:

Add '156.25' to each side of the equation.
-156.25 + -6.25x + 156.25 + x2 = 0 + 156.25

Reorder the terms:
-156.25 + 156.25 + -6.25x + x2 = 0 + 156.25

Combine like terms: -156.25 + 156.25 = 0.00
0.00 + -6.25x + x2 = 0 + 156.25
-6.25x + x2 = 0 + 156.25

Combine like terms: 0 + 156.25 = 156.25
-6.25x + x2 = 156.25

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = 156.25 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = 156.25 + 9.765625

Combine like terms: 156.25 + 9.765625 = 166.015625
9.765625 + -6.25x + x2 = 166.015625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 166.015625

Calculate the square root of the right side: 12.88470508

Break this problem into two subproblems by setting 
(x + -3.125) equal to 12.88470508 and -12.88470508.


Subproblem 1
x + -3.125 = 12.88470508

Simplifying
x + -3.125 = 12.88470508

Reorder the terms:
-3.125 + x = 12.88470508

Solving
-3.125 + x = 12.88470508

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = 12.88470508 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = 12.88470508 + 3.125
x = 12.88470508 + 3.125

Combine like terms: 12.88470508 + 3.125 = 16.00970508
x = 16.00970508

Simplifying
x = 16.00970508


Subproblem 2
x + -3.125 = -12.88470508

Simplifying
x + -3.125 = -12.88470508

Reorder the terms:
-3.125 + x = -12.88470508

Solving
-3.125 + x = -12.88470508

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = -12.88470508 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = -12.88470508 + 3.125
x = -12.88470508 + 3.125

Combine like terms: -12.88470508 + 3.125 = -9.75970508
x = -9.75970508

Simplifying
x = -9.75970508


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.00970508, -9.75970508}
Solution
x = {16.00970508, -9.75970508}

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