3p^2-18p+14=0

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Solution for 3p^2-18p+14=0 equation:


Simplifying
3p2 + -18p + 14 = 0

Reorder the terms:
14 + -18p + 3p2 = 0

Solving
14 + -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'.
4.666666667 + -6p + p2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + -6p + -4.666666667 + p2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + -6p + p2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + -6p + p2 = 0 + -4.666666667
-6p + p2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
-6p + p2 = -4.666666667

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 = -4.666666667 + 9

Reorder the terms:
9 + -6p + p2 = -4.666666667 + 9

Combine like terms: -4.666666667 + 9 = 4.333333333
9 + -6p + p2 = 4.333333333

Factor a perfect square on the left side:
(p + -3)(p + -3) = 4.333333333

Calculate the square root of the right side: 2.081665999

Break this problem into two subproblems by setting 
(p + -3) equal to 2.081665999 and -2.081665999.

Subproblem 1

p + -3 = 2.081665999 Simplifying p + -3 = 2.081665999 Reorder the terms: -3 + p = 2.081665999 Solving -3 + p = 2.081665999 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 = 2.081665999 + 3 Combine like terms: -3 + 3 = 0 0 + p = 2.081665999 + 3 p = 2.081665999 + 3 Combine like terms: 2.081665999 + 3 = 5.081665999 p = 5.081665999 Simplifying p = 5.081665999

Subproblem 2

p + -3 = -2.081665999 Simplifying p + -3 = -2.081665999 Reorder the terms: -3 + p = -2.081665999 Solving -3 + p = -2.081665999 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 = -2.081665999 + 3 Combine like terms: -3 + 3 = 0 0 + p = -2.081665999 + 3 p = -2.081665999 + 3 Combine like terms: -2.081665999 + 3 = 0.918334001 p = 0.918334001 Simplifying p = 0.918334001

Solution

The solution to the problem is based on the solutions from the subproblems. p = {5.081665999, 0.918334001}

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