3p^2+18p+2=0

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Solution for 3p^2+18p+2=0 equation: 


Simplifying
3p2 + 18p + 2 = 0

Reorder the terms:
2 + 18p + 3p2 = 0

Solving
2 + 18p + 3p2 = 0

Solving for variable 'p'.

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

Divide each side by '3'.
0.6666666667 + 6p + p2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 6p + -0.6666666667 + p2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 6p + p2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 6p + p2 = 0 + -0.6666666667
6p + p2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
6p + p2 = -0.6666666667

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

Add '9' to each side of the equation.
6p + 9 + p2 = -0.6666666667 + 9

Reorder the terms:
9 + 6p + p2 = -0.6666666667 + 9

Combine like terms: -0.6666666667 + 9 = 8.3333333333
9 + 6p + p2 = 8.3333333333

Factor a perfect square on the left side:
(p + 3)(p + 3) = 8.3333333333

Calculate the square root of the right side: 2.886751346

Break this problem into two subproblems by setting 
(p + 3) equal to 2.886751346 and -2.886751346.


Subproblem 1
p + 3 = 2.886751346

Simplifying
p + 3 = 2.886751346

Reorder the terms:
3 + p = 2.886751346

Solving
3 + p = 2.886751346

Solving for variable 'p'.

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

Add '-3' to each side of the equation.
3 + -3 + p = 2.886751346 + -3

Combine like terms: 3 + -3 = 0
0 + p = 2.886751346 + -3
p = 2.886751346 + -3

Combine like terms: 2.886751346 + -3 = -0.113248654
p = -0.113248654

Simplifying
p = -0.113248654


Subproblem 2
p + 3 = -2.886751346

Simplifying
p + 3 = -2.886751346

Reorder the terms:
3 + p = -2.886751346

Solving
3 + p = -2.886751346

Solving for variable 'p'.

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

Add '-3' to each side of the equation.
3 + -3 + p = -2.886751346 + -3

Combine like terms: 3 + -3 = 0
0 + p = -2.886751346 + -3
p = -2.886751346 + -3

Combine like terms: -2.886751346 + -3 = -5.886751346
p = -5.886751346

Simplifying
p = -5.886751346


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.113248654, -5.886751346}

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