p^2+2p-219=0

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Solution for p^2+2p-219=0 equation:


Simplifying
p2 + 2p + -219 = 0

Reorder the terms:
-219 + 2p + p2 = 0

Solving
-219 + 2p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '219' to each side of the equation.
-219 + 2p + 219 + p2 = 0 + 219

Reorder the terms:
-219 + 219 + 2p + p2 = 0 + 219

Combine like terms: -219 + 219 = 0
0 + 2p + p2 = 0 + 219
2p + p2 = 0 + 219

Combine like terms: 0 + 219 = 219
2p + p2 = 219

The p term is 2p.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2p + 1 + p2 = 219 + 1

Reorder the terms:
1 + 2p + p2 = 219 + 1

Combine like terms: 219 + 1 = 220
1 + 2p + p2 = 220

Factor a perfect square on the left side:
(p + 1)(p + 1) = 220

Calculate the square root of the right side: 14.832396974

Break this problem into two subproblems by setting 
(p + 1) equal to 14.832396974 and -14.832396974.

Subproblem 1

p + 1 = 14.832396974 Simplifying p + 1 = 14.832396974 Reorder the terms: 1 + p = 14.832396974 Solving 1 + p = 14.832396974 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 14.832396974 + -1 Combine like terms: 1 + -1 = 0 0 + p = 14.832396974 + -1 p = 14.832396974 + -1 Combine like terms: 14.832396974 + -1 = 13.832396974 p = 13.832396974 Simplifying p = 13.832396974

Subproblem 2

p + 1 = -14.832396974 Simplifying p + 1 = -14.832396974 Reorder the terms: 1 + p = -14.832396974 Solving 1 + p = -14.832396974 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = -14.832396974 + -1 Combine like terms: 1 + -1 = 0 0 + p = -14.832396974 + -1 p = -14.832396974 + -1 Combine like terms: -14.832396974 + -1 = -15.832396974 p = -15.832396974 Simplifying p = -15.832396974

Solution

The solution to the problem is based on the solutions from the subproblems. p = {13.832396974, -15.832396974}

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