2x^2+24x+63=0

Solution for 2x^2+24x+63=0 equation:

Simplifying
2x2 + 24x + 63 = 0

Reorder the terms:
63 + 24x + 2x2 = 0

Solving
63 + 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'.
31.5 + 12x + x2 = 0

Move the constant term to the right:

Add '-31.5' to each side of the equation.
31.5 + 12x + -31.5 + x2 = 0 + -31.5

Reorder the terms:
31.5 + -31.5 + 12x + x2 = 0 + -31.5

Combine like terms: 31.5 + -31.5 = 0.0
0.0 + 12x + x2 = 0 + -31.5
12x + x2 = 0 + -31.5

Combine like terms: 0 + -31.5 = -31.5
12x + x2 = -31.5

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 = -31.5 + 36

Reorder the terms:
36 + 12x + x2 = -31.5 + 36

Combine like terms: -31.5 + 36 = 4.5
36 + 12x + x2 = 4.5

Factor a perfect square on the left side:
(x + 6)(x + 6) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(x + 6) equal to 2.121320344 and -2.121320344.

Subproblem 1
x + 6 = 2.121320344

Simplifying
x + 6 = 2.121320344

Reorder the terms:
6 + x = 2.121320344

Solving
6 + x = 2.121320344

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 = 2.121320344 + -6

Combine like terms: 6 + -6 = 0
0 + x = 2.121320344 + -6
x = 2.121320344 + -6

Combine like terms: 2.121320344 + -6 = -3.878679656
x = -3.878679656

Simplifying
x = -3.878679656

Subproblem 2
x + 6 = -2.121320344

Simplifying
x + 6 = -2.121320344

Reorder the terms:
6 + x = -2.121320344

Solving
6 + x = -2.121320344

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 = -2.121320344 + -6

Combine like terms: 6 + -6 = 0
0 + x = -2.121320344 + -6
x = -2.121320344 + -6

Combine like terms: -2.121320344 + -6 = -8.121320344
x = -8.121320344

Simplifying
x = -8.121320344

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.878679656, -8.121320344}