3x^2+60x+66=0

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Solution for 3x^2+60x+66=0 equation: 


Simplifying
3x2 + 60x + 66 = 0

Reorder the terms:
66 + 60x + 3x2 = 0

Solving
66 + 60x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(22 + 20x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(22 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
22 + 20x + x2 = 0

Solving
22 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + 20x + -22 + x2 = 0 + -22

Reorder the terms:
22 + -22 + 20x + x2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 20x + x2 = 0 + -22
20x + x2 = 0 + -22

Combine like terms: 0 + -22 = -22
20x + x2 = -22

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -22 + 100

Reorder the terms:
100 + 20x + x2 = -22 + 100

Combine like terms: -22 + 100 = 78
100 + 20x + x2 = 78

Factor a perfect square on the left side:
(x + 10)(x + 10) = 78

Calculate the square root of the right side: 8.831760866

Break this problem into two subproblems by setting 
(x + 10) equal to 8.831760866 and -8.831760866.


Subproblem 1
x + 10 = 8.831760866

Simplifying
x + 10 = 8.831760866

Reorder the terms:
10 + x = 8.831760866

Solving
10 + x = 8.831760866

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 8.831760866 + -10

Combine like terms: 10 + -10 = 0
0 + x = 8.831760866 + -10
x = 8.831760866 + -10

Combine like terms: 8.831760866 + -10 = -1.168239134
x = -1.168239134

Simplifying
x = -1.168239134


Subproblem 2
x + 10 = -8.831760866

Simplifying
x + 10 = -8.831760866

Reorder the terms:
10 + x = -8.831760866

Solving
10 + x = -8.831760866

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -8.831760866 + -10

Combine like terms: 10 + -10 = 0
0 + x = -8.831760866 + -10
x = -8.831760866 + -10

Combine like terms: -8.831760866 + -10 = -18.831760866
x = -18.831760866

Simplifying
x = -18.831760866


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.168239134, -18.831760866}
Solution
x = {-1.168239134, -18.831760866}

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