2p^2+20p-25=0

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Solution for 2p^2+20p-25=0 equation:


Simplifying
2p2 + 20p + -25 = 0

Reorder the terms:
-25 + 20p + 2p2 = 0

Solving
-25 + 20p + 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'.
-12.5 + 10p + p2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + 10p + 12.5 + p2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + 10p + p2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + 10p + p2 = 0 + 12.5
10p + p2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
10p + p2 = 12.5

The p term is 10p.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10p + 25 + p2 = 12.5 + 25

Reorder the terms:
25 + 10p + p2 = 12.5 + 25

Combine like terms: 12.5 + 25 = 37.5
25 + 10p + p2 = 37.5

Factor a perfect square on the left side:
(p + 5)(p + 5) = 37.5

Calculate the square root of the right side: 6.123724357

Break this problem into two subproblems by setting 
(p + 5) equal to 6.123724357 and -6.123724357.

Subproblem 1

p + 5 = 6.123724357 Simplifying p + 5 = 6.123724357 Reorder the terms: 5 + p = 6.123724357 Solving 5 + p = 6.123724357 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = 6.123724357 + -5 Combine like terms: 5 + -5 = 0 0 + p = 6.123724357 + -5 p = 6.123724357 + -5 Combine like terms: 6.123724357 + -5 = 1.123724357 p = 1.123724357 Simplifying p = 1.123724357

Subproblem 2

p + 5 = -6.123724357 Simplifying p + 5 = -6.123724357 Reorder the terms: 5 + p = -6.123724357 Solving 5 + p = -6.123724357 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = -6.123724357 + -5 Combine like terms: 5 + -5 = 0 0 + p = -6.123724357 + -5 p = -6.123724357 + -5 Combine like terms: -6.123724357 + -5 = -11.123724357 p = -11.123724357 Simplifying p = -11.123724357

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.123724357, -11.123724357}

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