x^2-20x-81=0

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Solution for x^2-20x-81=0 equation: 


Simplifying
x2 + -20x + -81 = 0

Reorder the terms:
-81 + -20x + x2 = 0

Solving
-81 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + -20x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + -20x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -20x + x2 = 0 + 81
-20x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
-20x + x2 = 81

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 = 81 + 100

Reorder the terms:
100 + -20x + x2 = 81 + 100

Combine like terms: 81 + 100 = 181
100 + -20x + x2 = 181

Factor a perfect square on the left side:
(x + -10)(x + -10) = 181

Calculate the square root of the right side: 13.453624047

Break this problem into two subproblems by setting 
(x + -10) equal to 13.453624047 and -13.453624047.


Subproblem 1
x + -10 = 13.453624047

Simplifying
x + -10 = 13.453624047

Reorder the terms:
-10 + x = 13.453624047

Solving
-10 + x = 13.453624047

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 = 13.453624047 + 10

Combine like terms: -10 + 10 = 0
0 + x = 13.453624047 + 10
x = 13.453624047 + 10

Combine like terms: 13.453624047 + 10 = 23.453624047
x = 23.453624047

Simplifying
x = 23.453624047


Subproblem 2
x + -10 = -13.453624047

Simplifying
x + -10 = -13.453624047

Reorder the terms:
-10 + x = -13.453624047

Solving
-10 + x = -13.453624047

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 = -13.453624047 + 10

Combine like terms: -10 + 10 = 0
0 + x = -13.453624047 + 10
x = -13.453624047 + 10

Combine like terms: -13.453624047 + 10 = -3.453624047
x = -3.453624047

Simplifying
x = -3.453624047


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.453624047, -3.453624047}

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