x^2-20x-6=0

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Solution for x^2-20x-6=0 equation: 


Simplifying
x2 + -20x + -6 = 0

Reorder the terms:
-6 + -20x + x2 = 0

Solving
-6 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -20x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -20x + x2 = 0 + 6

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

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

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 = 6 + 100

Reorder the terms:
100 + -20x + x2 = 6 + 100

Combine like terms: 6 + 100 = 106
100 + -20x + x2 = 106

Factor a perfect square on the left side:
(x + -10)(x + -10) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + -10) equal to 10.295630141 and -10.295630141.


Subproblem 1
x + -10 = 10.295630141

Simplifying
x + -10 = 10.295630141

Reorder the terms:
-10 + x = 10.295630141

Solving
-10 + x = 10.295630141

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 = 10.295630141 + 10

Combine like terms: -10 + 10 = 0
0 + x = 10.295630141 + 10
x = 10.295630141 + 10

Combine like terms: 10.295630141 + 10 = 20.295630141
x = 20.295630141

Simplifying
x = 20.295630141


Subproblem 2
x + -10 = -10.295630141

Simplifying
x + -10 = -10.295630141

Reorder the terms:
-10 + x = -10.295630141

Solving
-10 + x = -10.295630141

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 = -10.295630141 + 10

Combine like terms: -10 + 10 = 0
0 + x = -10.295630141 + 10
x = -10.295630141 + 10

Combine like terms: -10.295630141 + 10 = -0.295630141
x = -0.295630141

Simplifying
x = -0.295630141


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.295630141, -0.295630141}

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