15p+3p^2=20

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Solution for 15p+3p^2=20 equation:


Simplifying
15p + 3p2 = 20

Solving
15p + 3p2 = 20

Solving for variable 'p'.

Reorder the terms:
-20 + 15p + 3p2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 15p + 3p2 = 0

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

Divide each side by '3'.
-6.666666667 + 5p + p2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + 5p + 6.666666667 + p2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + 5p + p2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + 5p + p2 = 0 + 6.666666667
5p + p2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
5p + p2 = 6.666666667

The p term is 5p.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5p + 6.25 + p2 = 6.666666667 + 6.25

Reorder the terms:
6.25 + 5p + p2 = 6.666666667 + 6.25

Combine like terms: 6.666666667 + 6.25 = 12.916666667
6.25 + 5p + p2 = 12.916666667

Factor a perfect square on the left side:
(p + 2.5)(p + 2.5) = 12.916666667

Calculate the square root of the right side: 3.593976442

Break this problem into two subproblems by setting 
(p + 2.5) equal to 3.593976442 and -3.593976442.

Subproblem 1

p + 2.5 = 3.593976442 Simplifying p + 2.5 = 3.593976442 Reorder the terms: 2.5 + p = 3.593976442 Solving 2.5 + p = 3.593976442 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = 3.593976442 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = 3.593976442 + -2.5 p = 3.593976442 + -2.5 Combine like terms: 3.593976442 + -2.5 = 1.093976442 p = 1.093976442 Simplifying p = 1.093976442

Subproblem 2

p + 2.5 = -3.593976442 Simplifying p + 2.5 = -3.593976442 Reorder the terms: 2.5 + p = -3.593976442 Solving 2.5 + p = -3.593976442 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = -3.593976442 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = -3.593976442 + -2.5 p = -3.593976442 + -2.5 Combine like terms: -3.593976442 + -2.5 = -6.093976442 p = -6.093976442 Simplifying p = -6.093976442

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.093976442, -6.093976442}

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