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Simplifying p(2p + p2 + -4) = 0 Reorder the terms: p(-4 + 2p + p2) = 0 (-4 * p + 2p * p + p2 * p) = 0 (-4p + 2p2 + p3) = 0 Solving -4p + 2p2 + p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(-4 + 2p + p2) = 0Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(-4 + 2p + p2)' equal to zero and attempt to solve: Simplifying -4 + 2p + p2 = 0 Solving -4 + 2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 2p + 4 + p2 = 0 + 4 Reorder the terms: -4 + 4 + 2p + p2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2p + p2 = 0 + 4 2p + p2 = 0 + 4 Combine like terms: 0 + 4 = 4 2p + p2 = 4 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 = 4 + 1 Reorder the terms: 1 + 2p + p2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + 2p + p2 = 5 Factor a perfect square on the left side: (p + 1)(p + 1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (p + 1) equal to 2.236067978 and -2.236067978.Subproblem 1
p + 1 = 2.236067978 Simplifying p + 1 = 2.236067978 Reorder the terms: 1 + p = 2.236067978 Solving 1 + p = 2.236067978 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 = 2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + p = 2.236067978 + -1 p = 2.236067978 + -1 Combine like terms: 2.236067978 + -1 = 1.236067978 p = 1.236067978 Simplifying p = 1.236067978Subproblem 2
p + 1 = -2.236067978 Simplifying p + 1 = -2.236067978 Reorder the terms: 1 + p = -2.236067978 Solving 1 + p = -2.236067978 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 = -2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + p = -2.236067978 + -1 p = -2.236067978 + -1 Combine like terms: -2.236067978 + -1 = -3.236067978 p = -3.236067978 Simplifying p = -3.236067978Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.236067978, -3.236067978}Solution
p = {0, 1.236067978, -3.236067978}
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