-3x^2-66x-356=0

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Solution for -3x^2-66x-356=0 equation: 


Simplifying
-3x2 + -66x + -356 = 0

Reorder the terms:
-356 + -66x + -3x2 = 0

Solving
-356 + -66x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(356 + 66x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(356 + 66x + 3x2)' equal to zero and attempt to solve:

Simplifying
356 + 66x + 3x2 = 0

Solving
356 + 66x + 3x2 = 0

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

Divide each side by '3'.
118.6666667 + 22x + x2 = 0

Move the constant term to the right:

Add '-118.6666667' to each side of the equation.
118.6666667 + 22x + -118.6666667 + x2 = 0 + -118.6666667

Reorder the terms:
118.6666667 + -118.6666667 + 22x + x2 = 0 + -118.6666667

Combine like terms: 118.6666667 + -118.6666667 = 0.0000000
0.0000000 + 22x + x2 = 0 + -118.6666667
22x + x2 = 0 + -118.6666667

Combine like terms: 0 + -118.6666667 = -118.6666667
22x + x2 = -118.6666667

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = -118.6666667 + 121

Reorder the terms:
121 + 22x + x2 = -118.6666667 + 121

Combine like terms: -118.6666667 + 121 = 2.3333333
121 + 22x + x2 = 2.3333333

Factor a perfect square on the left side:
(x + 11)(x + 11) = 2.3333333

Calculate the square root of the right side: 1.527525221

Break this problem into two subproblems by setting 
(x + 11) equal to 1.527525221 and -1.527525221.


Subproblem 1
x + 11 = 1.527525221

Simplifying
x + 11 = 1.527525221

Reorder the terms:
11 + x = 1.527525221

Solving
11 + x = 1.527525221

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 1.527525221 + -11

Combine like terms: 11 + -11 = 0
0 + x = 1.527525221 + -11
x = 1.527525221 + -11

Combine like terms: 1.527525221 + -11 = -9.472474779
x = -9.472474779

Simplifying
x = -9.472474779


Subproblem 2
x + 11 = -1.527525221

Simplifying
x + 11 = -1.527525221

Reorder the terms:
11 + x = -1.527525221

Solving
11 + x = -1.527525221

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -1.527525221 + -11

Combine like terms: 11 + -11 = 0
0 + x = -1.527525221 + -11
x = -1.527525221 + -11

Combine like terms: -1.527525221 + -11 = -12.527525221
x = -12.527525221

Simplifying
x = -12.527525221


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-9.472474779, -12.527525221}
Solution
x = {-9.472474779, -12.527525221}

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