2p^2+18p+13=0

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Solution for 2p^2+18p+13=0 equation:


Simplifying
2p2 + 18p + 13 = 0

Reorder the terms:
13 + 18p + 2p2 = 0

Solving
13 + 18p + 2p2 = 0

Solving for variable 'p'.

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

Divide each side by '2'.
6.5 + 9p + p2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + 9p + -6.5 + p2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + 9p + p2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + 9p + p2 = 0 + -6.5
9p + p2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
9p + p2 = -6.5

The p term is 9p.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9p + 20.25 + p2 = -6.5 + 20.25

Reorder the terms:
20.25 + 9p + p2 = -6.5 + 20.25

Combine like terms: -6.5 + 20.25 = 13.75
20.25 + 9p + p2 = 13.75

Factor a perfect square on the left side:
(p + 4.5)(p + 4.5) = 13.75

Calculate the square root of the right side: 3.708099244

Break this problem into two subproblems by setting 
(p + 4.5) equal to 3.708099244 and -3.708099244.

Subproblem 1

p + 4.5 = 3.708099244 Simplifying p + 4.5 = 3.708099244 Reorder the terms: 4.5 + p = 3.708099244 Solving 4.5 + p = 3.708099244 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + p = 3.708099244 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = 3.708099244 + -4.5 p = 3.708099244 + -4.5 Combine like terms: 3.708099244 + -4.5 = -0.791900756 p = -0.791900756 Simplifying p = -0.791900756

Subproblem 2

p + 4.5 = -3.708099244 Simplifying p + 4.5 = -3.708099244 Reorder the terms: 4.5 + p = -3.708099244 Solving 4.5 + p = -3.708099244 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + p = -3.708099244 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = -3.708099244 + -4.5 p = -3.708099244 + -4.5 Combine like terms: -3.708099244 + -4.5 = -8.208099244 p = -8.208099244 Simplifying p = -8.208099244

Solution

The solution to the problem is based on the solutions from the subproblems. p = {-0.791900756, -8.208099244}

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