4x^2-100x-16=0

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Solution for 4x^2-100x-16=0 equation: 


Simplifying
4x2 + -100x + -16 = 0

Reorder the terms:
-16 + -100x + 4x2 = 0

Solving
-16 + -100x + 4x2 = 0

Solving for variable 'x'.

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

Ignore the factor 4.

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

Simplifying
-4 + -25x + x2 = 0

Solving
-4 + -25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -25x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -25x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -25x + x2 = 0 + 4
-25x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-25x + x2 = 4

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = 4 + 156.25

Reorder the terms:
156.25 + -25x + x2 = 4 + 156.25

Combine like terms: 4 + 156.25 = 160.25
156.25 + -25x + x2 = 160.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 160.25

Calculate the square root of the right side: 12.658988901

Break this problem into two subproblems by setting 
(x + -12.5) equal to 12.658988901 and -12.658988901.


Subproblem 1
x + -12.5 = 12.658988901

Simplifying
x + -12.5 = 12.658988901

Reorder the terms:
-12.5 + x = 12.658988901

Solving
-12.5 + x = 12.658988901

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = 12.658988901 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 12.658988901 + 12.5
x = 12.658988901 + 12.5

Combine like terms: 12.658988901 + 12.5 = 25.158988901
x = 25.158988901

Simplifying
x = 25.158988901


Subproblem 2
x + -12.5 = -12.658988901

Simplifying
x + -12.5 = -12.658988901

Reorder the terms:
-12.5 + x = -12.658988901

Solving
-12.5 + x = -12.658988901

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = -12.658988901 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -12.658988901 + 12.5
x = -12.658988901 + 12.5

Combine like terms: -12.658988901 + 12.5 = -0.158988901
x = -0.158988901

Simplifying
x = -0.158988901


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.158988901, -0.158988901}
Solution
x = {25.158988901, -0.158988901}

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