x^2-2x-51=0

Solution for x^2-2x-51=0 equation:

Simplifying
x2 + -2x + -51 = 0

Reorder the terms:
-51 + -2x + x2 = 0

Solving
-51 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + -2x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + -2x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -2x + x2 = 0 + 51
-2x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
-2x + x2 = 51

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 = 51 + 1

Reorder the terms:
1 + -2x + x2 = 51 + 1

Combine like terms: 51 + 1 = 52
1 + -2x + x2 = 52

Factor a perfect square on the left side:
(x + -1)(x + -1) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + -1) equal to 7.211102551 and -7.211102551.

Subproblem 1
x + -1 = 7.211102551

Simplifying
x + -1 = 7.211102551

Reorder the terms:
-1 + x = 7.211102551

Solving
-1 + x = 7.211102551

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 = 7.211102551 + 1

Combine like terms: -1 + 1 = 0
0 + x = 7.211102551 + 1
x = 7.211102551 + 1

Combine like terms: 7.211102551 + 1 = 8.211102551
x = 8.211102551

Simplifying
x = 8.211102551

Subproblem 2
x + -1 = -7.211102551

Simplifying
x + -1 = -7.211102551

Reorder the terms:
-1 + x = -7.211102551

Solving
-1 + x = -7.211102551

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 = -7.211102551 + 1

Combine like terms: -1 + 1 = 0
0 + x = -7.211102551 + 1
x = -7.211102551 + 1

Combine like terms: -7.211102551 + 1 = -6.211102551
x = -6.211102551

Simplifying
x = -6.211102551

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.211102551, -6.211102551}