x^2-2x-5=0

Solution for x^2-2x-5=0 equation:

Simplifying
x2 + -2x + -5 = 0

Reorder the terms:
-5 + -2x + x2 = 0

Solving
-5 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -2x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -2x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x + x2 = 0 + 5
-2x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2x + x2 = 5

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 = 5 + 1

Reorder the terms:
1 + -2x + x2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + -2x + x2 = 6

Factor a perfect square on the left side:
(x + -1)(x + -1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -1) equal to 2.449489743 and -2.449489743.

Subproblem 1
x + -1 = 2.449489743

Simplifying
x + -1 = 2.449489743

Reorder the terms:
-1 + x = 2.449489743

Solving
-1 + x = 2.449489743

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 = 2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.449489743 + 1
x = 2.449489743 + 1

Combine like terms: 2.449489743 + 1 = 3.449489743
x = 3.449489743

Simplifying
x = 3.449489743

Subproblem 2
x + -1 = -2.449489743

Simplifying
x + -1 = -2.449489743

Reorder the terms:
-1 + x = -2.449489743

Solving
-1 + x = -2.449489743

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 = -2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.449489743 + 1
x = -2.449489743 + 1

Combine like terms: -2.449489743 + 1 = -1.449489743
x = -1.449489743

Simplifying
x = -1.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.449489743, -1.449489743}