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 = 26.75
20.25 + 9p + p2 = 26.75

Factor a perfect square on the left side:
(p + 4.5)(p + 4.5) = 26.75

Calculate the square root of the right side: 5.172040216

Break this problem into two subproblems by setting 
(p + 4.5) equal to 5.172040216 and -5.172040216.

Subproblem 1

p + 4.5 = 5.172040216 Simplifying p + 4.5 = 5.172040216 Reorder the terms: 4.5 + p = 5.172040216 Solving 4.5 + p = 5.172040216 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 = 5.172040216 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = 5.172040216 + -4.5 p = 5.172040216 + -4.5 Combine like terms: 5.172040216 + -4.5 = 0.672040216 p = 0.672040216 Simplifying p = 0.672040216

Subproblem 2

p + 4.5 = -5.172040216 Simplifying p + 4.5 = -5.172040216 Reorder the terms: 4.5 + p = -5.172040216 Solving 4.5 + p = -5.172040216 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 = -5.172040216 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = -5.172040216 + -4.5 p = -5.172040216 + -4.5 Combine like terms: -5.172040216 + -4.5 = -9.672040216 p = -9.672040216 Simplifying p = -9.672040216

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.672040216, -9.672040216}

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