2x^2+24x-365=0

Solution for 2x^2+24x-365=0 equation:

Simplifying
2x2 + 24x + -365 = 0

Reorder the terms:
-365 + 24x + 2x2 = 0

Solving
-365 + 24x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-182.5 + 12x + x2 = 0

Move the constant term to the right:

Add '182.5' to each side of the equation.
-182.5 + 12x + 182.5 + x2 = 0 + 182.5

Reorder the terms:
-182.5 + 182.5 + 12x + x2 = 0 + 182.5

Combine like terms: -182.5 + 182.5 = 0.0
0.0 + 12x + x2 = 0 + 182.5
12x + x2 = 0 + 182.5

Combine like terms: 0 + 182.5 = 182.5
12x + x2 = 182.5

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 182.5 + 36

Reorder the terms:
36 + 12x + x2 = 182.5 + 36

Combine like terms: 182.5 + 36 = 218.5
36 + 12x + x2 = 218.5

Factor a perfect square on the left side:
(x + 6)(x + 6) = 218.5

Calculate the square root of the right side: 14.781745499

Break this problem into two subproblems by setting 
(x + 6) equal to 14.781745499 and -14.781745499.

Subproblem 1
x + 6 = 14.781745499

Simplifying
x + 6 = 14.781745499

Reorder the terms:
6 + x = 14.781745499

Solving
6 + x = 14.781745499

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 14.781745499 + -6

Combine like terms: 6 + -6 = 0
0 + x = 14.781745499 + -6
x = 14.781745499 + -6

Combine like terms: 14.781745499 + -6 = 8.781745499
x = 8.781745499

Simplifying
x = 8.781745499

Subproblem 2
x + 6 = -14.781745499

Simplifying
x + 6 = -14.781745499

Reorder the terms:
6 + x = -14.781745499

Solving
6 + x = -14.781745499

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -14.781745499 + -6

Combine like terms: 6 + -6 = 0
0 + x = -14.781745499 + -6
x = -14.781745499 + -6

Combine like terms: -14.781745499 + -6 = -20.781745499
x = -20.781745499

Simplifying
x = -20.781745499

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.781745499, -20.781745499}