2x^2-24x-27=0

Solution for 2x^2-24x-27=0 equation:

Simplifying
2x2 + -24x + -27 = 0

Reorder the terms:
-27 + -24x + 2x2 = 0

Solving
-27 + -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'.
-13.5 + -12x + x2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + -12x + 13.5 + x2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + -12x + x2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + -12x + x2 = 0 + 13.5
-12x + x2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
-12x + x2 = 13.5

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 = 13.5 + 36

Reorder the terms:
36 + -12x + x2 = 13.5 + 36

Combine like terms: 13.5 + 36 = 49.5
36 + -12x + x2 = 49.5

Factor a perfect square on the left side:
(x + -6)(x + -6) = 49.5

Calculate the square root of the right side: 7.03562364

Break this problem into two subproblems by setting 
(x + -6) equal to 7.03562364 and -7.03562364.

Subproblem 1
x + -6 = 7.03562364

Simplifying
x + -6 = 7.03562364

Reorder the terms:
-6 + x = 7.03562364

Solving
-6 + x = 7.03562364

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 = 7.03562364 + 6

Combine like terms: -6 + 6 = 0
0 + x = 7.03562364 + 6
x = 7.03562364 + 6

Combine like terms: 7.03562364 + 6 = 13.03562364
x = 13.03562364

Simplifying
x = 13.03562364

Subproblem 2
x + -6 = -7.03562364

Simplifying
x + -6 = -7.03562364

Reorder the terms:
-6 + x = -7.03562364

Solving
-6 + x = -7.03562364

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 = -7.03562364 + 6

Combine like terms: -6 + 6 = 0
0 + x = -7.03562364 + 6
x = -7.03562364 + 6

Combine like terms: -7.03562364 + 6 = -1.03562364
x = -1.03562364

Simplifying
x = -1.03562364

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.03562364, -1.03562364}