x^2-2x-31=0

Solution for x^2-2x-31=0 equation:

Simplifying
x2 + -2x + -31 = 0

Reorder the terms:
-31 + -2x + x2 = 0

Solving
-31 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -2x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + -2x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -2x + x2 = 0 + 31
-2x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
-2x + x2 = 31

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 = 31 + 1

Reorder the terms:
1 + -2x + x2 = 31 + 1

Combine like terms: 31 + 1 = 32
1 + -2x + x2 = 32

Factor a perfect square on the left side:
(x + -1)(x + -1) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + -1) equal to 5.656854249 and -5.656854249.

Subproblem 1
x + -1 = 5.656854249

Simplifying
x + -1 = 5.656854249

Reorder the terms:
-1 + x = 5.656854249

Solving
-1 + x = 5.656854249

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 = 5.656854249 + 1

Combine like terms: -1 + 1 = 0
0 + x = 5.656854249 + 1
x = 5.656854249 + 1

Combine like terms: 5.656854249 + 1 = 6.656854249
x = 6.656854249

Simplifying
x = 6.656854249

Subproblem 2
x + -1 = -5.656854249

Simplifying
x + -1 = -5.656854249

Reorder the terms:
-1 + x = -5.656854249

Solving
-1 + x = -5.656854249

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 = -5.656854249 + 1

Combine like terms: -1 + 1 = 0
0 + x = -5.656854249 + 1
x = -5.656854249 + 1

Combine like terms: -5.656854249 + 1 = -4.656854249
x = -4.656854249

Simplifying
x = -4.656854249

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.656854249, -4.656854249}