x^2-20x+39=0

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Solution for x^2-20x+39=0 equation: 


Simplifying
x2 + -20x + 39 = 0

Reorder the terms:
39 + -20x + x2 = 0

Solving
39 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + -20x + -39 + x2 = 0 + -39

Reorder the terms:
39 + -39 + -20x + x2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -20x + x2 = 0 + -39
-20x + x2 = 0 + -39

Combine like terms: 0 + -39 = -39
-20x + x2 = -39

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 = -39 + 100

Reorder the terms:
100 + -20x + x2 = -39 + 100

Combine like terms: -39 + 100 = 61
100 + -20x + x2 = 61

Factor a perfect square on the left side:
(x + -10)(x + -10) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(x + -10) equal to 7.810249676 and -7.810249676.


Subproblem 1
x + -10 = 7.810249676

Simplifying
x + -10 = 7.810249676

Reorder the terms:
-10 + x = 7.810249676

Solving
-10 + x = 7.810249676

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 = 7.810249676 + 10

Combine like terms: -10 + 10 = 0
0 + x = 7.810249676 + 10
x = 7.810249676 + 10

Combine like terms: 7.810249676 + 10 = 17.810249676
x = 17.810249676

Simplifying
x = 17.810249676


Subproblem 2
x + -10 = -7.810249676

Simplifying
x + -10 = -7.810249676

Reorder the terms:
-10 + x = -7.810249676

Solving
-10 + x = -7.810249676

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 = -7.810249676 + 10

Combine like terms: -10 + 10 = 0
0 + x = -7.810249676 + 10
x = -7.810249676 + 10

Combine like terms: -7.810249676 + 10 = 2.189750324
x = 2.189750324

Simplifying
x = 2.189750324


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.810249676, 2.189750324}

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