X^2-2X-59=0

Solution for X^2-2X-59=0 equation:

Simplifying
X2 + -2X + -59 = 0

Reorder the terms:
-59 + -2X + X2 = 0

Solving
-59 + -2X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + -2X + 59 + X2 = 0 + 59

Reorder the terms:
-59 + 59 + -2X + X2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + -2X + X2 = 0 + 59
-2X + X2 = 0 + 59

Combine like terms: 0 + 59 = 59
-2X + X2 = 59

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 = 59 + 1

Reorder the terms:
1 + -2X + X2 = 59 + 1

Combine like terms: 59 + 1 = 60
1 + -2X + X2 = 60

Factor a perfect square on the left side:
(X + -1)(X + -1) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(X + -1) equal to 7.745966692 and -7.745966692.

Subproblem 1
X + -1 = 7.745966692

Simplifying
X + -1 = 7.745966692

Reorder the terms:
-1 + X = 7.745966692

Solving
-1 + X = 7.745966692

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 = 7.745966692 + 1

Combine like terms: -1 + 1 = 0
0 + X = 7.745966692 + 1
X = 7.745966692 + 1

Combine like terms: 7.745966692 + 1 = 8.745966692
X = 8.745966692

Simplifying
X = 8.745966692

Subproblem 2
X + -1 = -7.745966692

Simplifying
X + -1 = -7.745966692

Reorder the terms:
-1 + X = -7.745966692

Solving
-1 + X = -7.745966692

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 = -7.745966692 + 1

Combine like terms: -1 + 1 = 0
0 + X = -7.745966692 + 1
X = -7.745966692 + 1

Combine like terms: -7.745966692 + 1 = -6.745966692
X = -6.745966692

Simplifying
X = -6.745966692

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {8.745966692, -6.745966692}