x^2-2x-23=0

Solution for x^2-2x-23=0 equation:

Simplifying
x2 + -2x + -23 = 0

Reorder the terms:
-23 + -2x + x2 = 0

Solving
-23 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + -2x + 23 + x2 = 0 + 23

Reorder the terms:
-23 + 23 + -2x + x2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -2x + x2 = 0 + 23
-2x + x2 = 0 + 23

Combine like terms: 0 + 23 = 23
-2x + x2 = 23

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 = 23 + 1

Reorder the terms:
1 + -2x + x2 = 23 + 1

Combine like terms: 23 + 1 = 24
1 + -2x + x2 = 24

Factor a perfect square on the left side:
(x + -1)(x + -1) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + -1) equal to 4.898979486 and -4.898979486.

Subproblem 1
x + -1 = 4.898979486

Simplifying
x + -1 = 4.898979486

Reorder the terms:
-1 + x = 4.898979486

Solving
-1 + x = 4.898979486

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 = 4.898979486 + 1

Combine like terms: -1 + 1 = 0
0 + x = 4.898979486 + 1
x = 4.898979486 + 1

Combine like terms: 4.898979486 + 1 = 5.898979486
x = 5.898979486

Simplifying
x = 5.898979486

Subproblem 2
x + -1 = -4.898979486

Simplifying
x + -1 = -4.898979486

Reorder the terms:
-1 + x = -4.898979486

Solving
-1 + x = -4.898979486

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 = -4.898979486 + 1

Combine like terms: -1 + 1 = 0
0 + x = -4.898979486 + 1
x = -4.898979486 + 1

Combine like terms: -4.898979486 + 1 = -3.898979486
x = -3.898979486

Simplifying
x = -3.898979486

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.898979486, -3.898979486}