3x^2+18x+20=0

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Solution for 3x^2+18x+20=0 equation: 


Simplifying
3x2 + 18x + 20 = 0

Reorder the terms:
20 + 18x + 3x2 = 0

Solving
20 + 18x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
6.666666667 + 6x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + 6x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + 6x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + 6x + x2 = 0 + -6.666666667
6x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
6x + x2 = -6.666666667

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -6.666666667 + 9

Reorder the terms:
9 + 6x + x2 = -6.666666667 + 9

Combine like terms: -6.666666667 + 9 = 2.333333333
9 + 6x + x2 = 2.333333333

Factor a perfect square on the left side:
(x + 3)(x + 3) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + 3) equal to 1.527525232 and -1.527525232.


Subproblem 1
x + 3 = 1.527525232

Simplifying
x + 3 = 1.527525232

Reorder the terms:
3 + x = 1.527525232

Solving
3 + x = 1.527525232

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 1.527525232 + -3

Combine like terms: 3 + -3 = 0
0 + x = 1.527525232 + -3
x = 1.527525232 + -3

Combine like terms: 1.527525232 + -3 = -1.472474768
x = -1.472474768

Simplifying
x = -1.472474768


Subproblem 2
x + 3 = -1.527525232

Simplifying
x + 3 = -1.527525232

Reorder the terms:
3 + x = -1.527525232

Solving
3 + x = -1.527525232

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -1.527525232 + -3

Combine like terms: 3 + -3 = 0
0 + x = -1.527525232 + -3
x = -1.527525232 + -3

Combine like terms: -1.527525232 + -3 = -4.527525232
x = -4.527525232

Simplifying
x = -4.527525232


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.472474768, -4.527525232}

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