x^2-6x-52=0

Solution for x^2-6x-52=0 equation:

Simplifying
x2 + -6x + -52 = 0

Reorder the terms:
-52 + -6x + x2 = 0

Solving
-52 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + -6x + 52 + x2 = 0 + 52

Reorder the terms:
-52 + 52 + -6x + x2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + -6x + x2 = 0 + 52
-6x + x2 = 0 + 52

Combine like terms: 0 + 52 = 52
-6x + x2 = 52

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 52 + 9

Reorder the terms:
9 + -6x + x2 = 52 + 9

Combine like terms: 52 + 9 = 61
9 + -6x + x2 = 61

Factor a perfect square on the left side:
(x + -3)(x + -3) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(x + -3) equal to 7.810249676 and -7.810249676.

Subproblem 1
x + -3 = 7.810249676

Simplifying
x + -3 = 7.810249676

Reorder the terms:
-3 + x = 7.810249676

Solving
-3 + x = 7.810249676

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + x = 7.810249676 + 3

Combine like terms: -3 + 3 = 0
0 + x = 7.810249676 + 3
x = 7.810249676 + 3

Combine like terms: 7.810249676 + 3 = 10.810249676
x = 10.810249676

Simplifying
x = 10.810249676

Subproblem 2
x + -3 = -7.810249676

Simplifying
x + -3 = -7.810249676

Reorder the terms:
-3 + x = -7.810249676

Solving
-3 + x = -7.810249676

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + x = -7.810249676 + 3

Combine like terms: -3 + 3 = 0
0 + x = -7.810249676 + 3
x = -7.810249676 + 3

Combine like terms: -7.810249676 + 3 = -4.810249676
x = -4.810249676

Simplifying
x = -4.810249676

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.810249676, -4.810249676}