x^2-2x-58=0

Solution for x^2-2x-58=0 equation:

Simplifying
x2 + -2x + -58 = 0

Reorder the terms:
-58 + -2x + x2 = 0

Solving
-58 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '58' to each side of the equation.
-58 + -2x + 58 + x2 = 0 + 58

Reorder the terms:
-58 + 58 + -2x + x2 = 0 + 58

Combine like terms: -58 + 58 = 0
0 + -2x + x2 = 0 + 58
-2x + x2 = 0 + 58

Combine like terms: 0 + 58 = 58
-2x + x2 = 58

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 = 58 + 1

Reorder the terms:
1 + -2x + x2 = 58 + 1

Combine like terms: 58 + 1 = 59
1 + -2x + x2 = 59

Factor a perfect square on the left side:
(x + -1)(x + -1) = 59

Calculate the square root of the right side: 7.681145748

Break this problem into two subproblems by setting 
(x + -1) equal to 7.681145748 and -7.681145748.

Subproblem 1
x + -1 = 7.681145748

Simplifying
x + -1 = 7.681145748

Reorder the terms:
-1 + x = 7.681145748

Solving
-1 + x = 7.681145748

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 = 7.681145748 + 1

Combine like terms: -1 + 1 = 0
0 + x = 7.681145748 + 1
x = 7.681145748 + 1

Combine like terms: 7.681145748 + 1 = 8.681145748
x = 8.681145748

Simplifying
x = 8.681145748

Subproblem 2
x + -1 = -7.681145748

Simplifying
x + -1 = -7.681145748

Reorder the terms:
-1 + x = -7.681145748

Solving
-1 + x = -7.681145748

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 = -7.681145748 + 1

Combine like terms: -1 + 1 = 0
0 + x = -7.681145748 + 1
x = -7.681145748 + 1

Combine like terms: -7.681145748 + 1 = -6.681145748
x = -6.681145748

Simplifying
x = -6.681145748

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.681145748, -6.681145748}