x^2-2x-83=0

Solution for x^2-2x-83=0 equation:

Simplifying
x2 + -2x + -83 = 0

Reorder the terms:
-83 + -2x + x2 = 0

Solving
-83 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '83' to each side of the equation.
-83 + -2x + 83 + x2 = 0 + 83

Reorder the terms:
-83 + 83 + -2x + x2 = 0 + 83

Combine like terms: -83 + 83 = 0
0 + -2x + x2 = 0 + 83
-2x + x2 = 0 + 83

Combine like terms: 0 + 83 = 83
-2x + x2 = 83

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 83 + 1

Reorder the terms:
1 + -2x + x2 = 83 + 1

Combine like terms: 83 + 1 = 84
1 + -2x + x2 = 84

Factor a perfect square on the left side:
(x + -1)(x + -1) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x + -1) equal to 9.16515139 and -9.16515139.

Subproblem 1
x + -1 = 9.16515139

Simplifying
x + -1 = 9.16515139

Reorder the terms:
-1 + x = 9.16515139

Solving
-1 + x = 9.16515139

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 9.16515139 + 1

Combine like terms: -1 + 1 = 0
0 + x = 9.16515139 + 1
x = 9.16515139 + 1

Combine like terms: 9.16515139 + 1 = 10.16515139
x = 10.16515139

Simplifying
x = 10.16515139

Subproblem 2
x + -1 = -9.16515139

Simplifying
x + -1 = -9.16515139

Reorder the terms:
-1 + x = -9.16515139

Solving
-1 + x = -9.16515139

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -9.16515139 + 1

Combine like terms: -1 + 1 = 0
0 + x = -9.16515139 + 1
x = -9.16515139 + 1

Combine like terms: -9.16515139 + 1 = -8.16515139
x = -8.16515139

Simplifying
x = -8.16515139

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.16515139, -8.16515139}