3p^2-12p-200=0

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Solution for 3p^2-12p-200=0 equation: 


Simplifying
3p2 + -12p + -200 = 0

Reorder the terms:
-200 + -12p + 3p2 = 0

Solving
-200 + -12p + 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'.
-66.66666667 + -4p + p2 = 0

Move the constant term to the right:

Add '66.66666667' to each side of the equation.
-66.66666667 + -4p + 66.66666667 + p2 = 0 + 66.66666667

Reorder the terms:
-66.66666667 + 66.66666667 + -4p + p2 = 0 + 66.66666667

Combine like terms: -66.66666667 + 66.66666667 = 0.00000000
0.00000000 + -4p + p2 = 0 + 66.66666667
-4p + p2 = 0 + 66.66666667

Combine like terms: 0 + 66.66666667 = 66.66666667
-4p + p2 = 66.66666667

The p term is -4p.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4p + 4 + p2 = 66.66666667 + 4

Reorder the terms:
4 + -4p + p2 = 66.66666667 + 4

Combine like terms: 66.66666667 + 4 = 70.66666667
4 + -4p + p2 = 70.66666667

Factor a perfect square on the left side:
(p + -2)(p + -2) = 70.66666667

Calculate the square root of the right side: 8.406346809

Break this problem into two subproblems by setting 
(p + -2) equal to 8.406346809 and -8.406346809.


Subproblem 1
p + -2 = 8.406346809

Simplifying
p + -2 = 8.406346809

Reorder the terms:
-2 + p = 8.406346809

Solving
-2 + p = 8.406346809

Solving for variable 'p'.

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

Add '2' to each side of the equation.
-2 + 2 + p = 8.406346809 + 2

Combine like terms: -2 + 2 = 0
0 + p = 8.406346809 + 2
p = 8.406346809 + 2

Combine like terms: 8.406346809 + 2 = 10.406346809
p = 10.406346809

Simplifying
p = 10.406346809


Subproblem 2
p + -2 = -8.406346809

Simplifying
p + -2 = -8.406346809

Reorder the terms:
-2 + p = -8.406346809

Solving
-2 + p = -8.406346809

Solving for variable 'p'.

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

Add '2' to each side of the equation.
-2 + 2 + p = -8.406346809 + 2

Combine like terms: -2 + 2 = 0
0 + p = -8.406346809 + 2
p = -8.406346809 + 2

Combine like terms: -8.406346809 + 2 = -6.406346809
p = -6.406346809

Simplifying
p = -6.406346809


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {10.406346809, -6.406346809}

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