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 = 152.25
156.25 + -25x + x2 = 152.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 152.25

Calculate the square root of the right side: 12.338962679

Break this problem into two subproblems by setting 
(x + -12.5) equal to 12.338962679 and -12.338962679.


Subproblem 1
x + -12.5 = 12.338962679

Simplifying
x + -12.5 = 12.338962679

Reorder the terms:
-12.5 + x = 12.338962679

Solving
-12.5 + x = 12.338962679

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 = 12.338962679 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 12.338962679 + 12.5
x = 12.338962679 + 12.5

Combine like terms: 12.338962679 + 12.5 = 24.838962679
x = 24.838962679

Simplifying
x = 24.838962679


Subproblem 2
x + -12.5 = -12.338962679

Simplifying
x + -12.5 = -12.338962679

Reorder the terms:
-12.5 + x = -12.338962679

Solving
-12.5 + x = -12.338962679

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 = -12.338962679 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -12.338962679 + 12.5
x = -12.338962679 + 12.5

Combine like terms: -12.338962679 + 12.5 = 0.161037321
x = 0.161037321

Simplifying
x = 0.161037321


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.838962679, 0.161037321}
Solution
x = {24.838962679, 0.161037321}

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