x^2-20x+13=0

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Solution for x^2-20x+13=0 equation: 


Simplifying
x2 + -20x + 13 = 0

Reorder the terms:
13 + -20x + x2 = 0

Solving
13 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -20x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + -20x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -20x + x2 = 0 + -13
-20x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-20x + x2 = -13

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -13 + 100

Reorder the terms:
100 + -20x + x2 = -13 + 100

Combine like terms: -13 + 100 = 87
100 + -20x + x2 = 87

Factor a perfect square on the left side:
(x + -10)(x + -10) = 87

Calculate the square root of the right side: 9.327379053

Break this problem into two subproblems by setting 
(x + -10) equal to 9.327379053 and -9.327379053.


Subproblem 1
x + -10 = 9.327379053

Simplifying
x + -10 = 9.327379053

Reorder the terms:
-10 + x = 9.327379053

Solving
-10 + x = 9.327379053

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 9.327379053 + 10

Combine like terms: -10 + 10 = 0
0 + x = 9.327379053 + 10
x = 9.327379053 + 10

Combine like terms: 9.327379053 + 10 = 19.327379053
x = 19.327379053

Simplifying
x = 19.327379053


Subproblem 2
x + -10 = -9.327379053

Simplifying
x + -10 = -9.327379053

Reorder the terms:
-10 + x = -9.327379053

Solving
-10 + x = -9.327379053

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -9.327379053 + 10

Combine like terms: -10 + 10 = 0
0 + x = -9.327379053 + 10
x = -9.327379053 + 10

Combine like terms: -9.327379053 + 10 = 0.672620947
x = 0.672620947

Simplifying
x = 0.672620947


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.327379053, 0.672620947}

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