0=x^2+66x+39

Solution for 0=x^2+66x+39 equation:

Simplifying
0 = x2 + 66x + 39

Reorder the terms:
0 = 39 + 66x + x2

Solving
0 = 39 + 66x + x2

Solving for variable 'x'.

Combine like terms: 0 + -39 = -39
-39 + -66x + -1x2 = 39 + 66x + x2 + -39 + -66x + -1x2

Reorder the terms:
-39 + -66x + -1x2 = 39 + -39 + 66x + -66x + x2 + -1x2

Combine like terms: 39 + -39 = 0
-39 + -66x + -1x2 = 0 + 66x + -66x + x2 + -1x2
-39 + -66x + -1x2 = 66x + -66x + x2 + -1x2

Combine like terms: 66x + -66x = 0
-39 + -66x + -1x2 = 0 + x2 + -1x2
-39 + -66x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-39 + -66x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(39 + 66x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(39 + 66x + x2)' equal to zero and attempt to solve:

Simplifying
39 + 66x + x2 = 0

Solving
39 + 66x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + 66x + -39 + x2 = 0 + -39

Reorder the terms:
39 + -39 + 66x + x2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + 66x + x2 = 0 + -39
66x + x2 = 0 + -39

Combine like terms: 0 + -39 = -39
66x + x2 = -39

The x term is 66x.  Take half its coefficient (33).
Square it (1089) and add it to both sides.

Add '1089' to each side of the equation.
66x + 1089 + x2 = -39 + 1089

Reorder the terms:
1089 + 66x + x2 = -39 + 1089

Combine like terms: -39 + 1089 = 1050
1089 + 66x + x2 = 1050

Factor a perfect square on the left side:
(x + 33)(x + 33) = 1050

Calculate the square root of the right side: 32.403703492

Break this problem into two subproblems by setting 
(x + 33) equal to 32.403703492 and -32.403703492.

Subproblem 1
x + 33 = 32.403703492

Simplifying
x + 33 = 32.403703492

Reorder the terms:
33 + x = 32.403703492

Solving
33 + x = 32.403703492

Solving for variable 'x'.

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

Add '-33' to each side of the equation.
33 + -33 + x = 32.403703492 + -33

Combine like terms: 33 + -33 = 0
0 + x = 32.403703492 + -33
x = 32.403703492 + -33

Combine like terms: 32.403703492 + -33 = -0.596296508
x = -0.596296508

Simplifying
x = -0.596296508

Subproblem 2
x + 33 = -32.403703492

Simplifying
x + 33 = -32.403703492

Reorder the terms:
33 + x = -32.403703492

Solving
33 + x = -32.403703492

Solving for variable 'x'.

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

Add '-33' to each side of the equation.
33 + -33 + x = -32.403703492 + -33

Combine like terms: 33 + -33 = 0
0 + x = -32.403703492 + -33
x = -32.403703492 + -33

Combine like terms: -32.403703492 + -33 = -65.403703492
x = -65.403703492

Simplifying
x = -65.403703492

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.596296508, -65.403703492}
Solution
x = {-0.596296508, -65.403703492}