x^2+6x-59=0

Solution for x^2+6x-59=0 equation:

Simplifying
x2 + 6x + -59 = 0

Reorder the terms:
-59 + 6x + x2 = 0

Solving
-59 + 6x + 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 + 6x + 59 + x2 = 0 + 59

Reorder the terms:
-59 + 59 + 6x + x2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + 6x + x2 = 0 + 59
6x + x2 = 0 + 59

Combine like terms: 0 + 59 = 59
6x + x2 = 59

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 = 59 + 9

Reorder the terms:
9 + 6x + x2 = 59 + 9

Combine like terms: 59 + 9 = 68
9 + 6x + x2 = 68

Factor a perfect square on the left side:
(x + 3)(x + 3) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(x + 3) equal to 8.246211251 and -8.246211251.

Subproblem 1
x + 3 = 8.246211251

Simplifying
x + 3 = 8.246211251

Reorder the terms:
3 + x = 8.246211251

Solving
3 + x = 8.246211251

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 = 8.246211251 + -3

Combine like terms: 3 + -3 = 0
0 + x = 8.246211251 + -3
x = 8.246211251 + -3

Combine like terms: 8.246211251 + -3 = 5.246211251
x = 5.246211251

Simplifying
x = 5.246211251

Subproblem 2
x + 3 = -8.246211251

Simplifying
x + 3 = -8.246211251

Reorder the terms:
3 + x = -8.246211251

Solving
3 + x = -8.246211251

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 = -8.246211251 + -3

Combine like terms: 3 + -3 = 0
0 + x = -8.246211251 + -3
x = -8.246211251 + -3

Combine like terms: -8.246211251 + -3 = -11.246211251
x = -11.246211251

Simplifying
x = -11.246211251

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.246211251, -11.246211251}