13x^2-80x+100=0

Solution for 13x^2-80x+100=0 equation:

Simplifying
13x2 + -80x + 100 = 0

Reorder the terms:
100 + -80x + 13x2 = 0

Solving
100 + -80x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
7.692307692 + -6.153846154x + x2 = 0

Move the constant term to the right:

Add '-7.692307692' to each side of the equation.
7.692307692 + -6.153846154x + -7.692307692 + x2 = 0 + -7.692307692

Reorder the terms:
7.692307692 + -7.692307692 + -6.153846154x + x2 = 0 + -7.692307692

Combine like terms: 7.692307692 + -7.692307692 = 0.000000000
0.000000000 + -6.153846154x + x2 = 0 + -7.692307692
-6.153846154x + x2 = 0 + -7.692307692

Combine like terms: 0 + -7.692307692 = -7.692307692
-6.153846154x + x2 = -7.692307692

The x term is -6.153846154x.  Take half its coefficient (-3.076923077).
Square it (9.467455622) and add it to both sides.

Add '9.467455622' to each side of the equation.
-6.153846154x + 9.467455622 + x2 = -7.692307692 + 9.467455622

Reorder the terms:
9.467455622 + -6.153846154x + x2 = -7.692307692 + 9.467455622

Combine like terms: -7.692307692 + 9.467455622 = 1.77514793
9.467455622 + -6.153846154x + x2 = 1.77514793

Factor a perfect square on the left side:
(x + -3.076923077)(x + -3.076923077) = 1.77514793

Calculate the square root of the right side: 1.332346775

Break this problem into two subproblems by setting 
(x + -3.076923077) equal to 1.332346775 and -1.332346775.

Subproblem 1
x + -3.076923077 = 1.332346775

Simplifying
x + -3.076923077 = 1.332346775

Reorder the terms:
-3.076923077 + x = 1.332346775

Solving
-3.076923077 + x = 1.332346775

Solving for variable 'x'.

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

Add '3.076923077' to each side of the equation.
-3.076923077 + 3.076923077 + x = 1.332346775 + 3.076923077

Combine like terms: -3.076923077 + 3.076923077 = 0.000000000
0.000000000 + x = 1.332346775 + 3.076923077
x = 1.332346775 + 3.076923077

Combine like terms: 1.332346775 + 3.076923077 = 4.409269852
x = 4.409269852

Simplifying
x = 4.409269852

Subproblem 2
x + -3.076923077 = -1.332346775

Simplifying
x + -3.076923077 = -1.332346775

Reorder the terms:
-3.076923077 + x = -1.332346775

Solving
-3.076923077 + x = -1.332346775

Solving for variable 'x'.

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

Add '3.076923077' to each side of the equation.
-3.076923077 + 3.076923077 + x = -1.332346775 + 3.076923077

Combine like terms: -3.076923077 + 3.076923077 = 0.000000000
0.000000000 + x = -1.332346775 + 3.076923077
x = -1.332346775 + 3.076923077

Combine like terms: -1.332346775 + 3.076923077 = 1.744576302
x = 1.744576302

Simplifying
x = 1.744576302

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.409269852, 1.744576302}