x^2-20x+13=6

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Solution for x^2-20x+13=6 equation: 


Simplifying
x2 + -20x + 13 = 6

Reorder the terms:
13 + -20x + x2 = 6

Solving
13 + -20x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
13 + -6 + -20x + x2 = 6 + -6

Combine like terms: 13 + -6 = 7
7 + -20x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
7 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -20x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -20x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -20x + x2 = 0 + -7
-20x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-20x + x2 = -7

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 = -7 + 100

Reorder the terms:
100 + -20x + x2 = -7 + 100

Combine like terms: -7 + 100 = 93
100 + -20x + x2 = 93

Factor a perfect square on the left side:
(x + -10)(x + -10) = 93

Calculate the square root of the right side: 9.643650761

Break this problem into two subproblems by setting 
(x + -10) equal to 9.643650761 and -9.643650761.


Subproblem 1
x + -10 = 9.643650761

Simplifying
x + -10 = 9.643650761

Reorder the terms:
-10 + x = 9.643650761

Solving
-10 + x = 9.643650761

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 = 9.643650761 + 10

Combine like terms: -10 + 10 = 0
0 + x = 9.643650761 + 10
x = 9.643650761 + 10

Combine like terms: 9.643650761 + 10 = 19.643650761
x = 19.643650761

Simplifying
x = 19.643650761


Subproblem 2
x + -10 = -9.643650761

Simplifying
x + -10 = -9.643650761

Reorder the terms:
-10 + x = -9.643650761

Solving
-10 + x = -9.643650761

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 = -9.643650761 + 10

Combine like terms: -10 + 10 = 0
0 + x = -9.643650761 + 10
x = -9.643650761 + 10

Combine like terms: -9.643650761 + 10 = 0.356349239
x = 0.356349239

Simplifying
x = 0.356349239


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.643650761, 0.356349239}

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