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Simplifying 2p2 = 2 + -8p Solving 2p2 = 2 + -8p Solving for variable 'p'. Reorder the terms: -2 + 8p + 2p2 = 2 + -8p + -2 + 8p Reorder the terms: -2 + 8p + 2p2 = 2 + -2 + -8p + 8p Combine like terms: 2 + -2 = 0 -2 + 8p + 2p2 = 0 + -8p + 8p -2 + 8p + 2p2 = -8p + 8p Combine like terms: -8p + 8p = 0 -2 + 8p + 2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 4p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 4p + p2)' equal to zero and attempt to solve: Simplifying -1 + 4p + p2 = 0 Solving -1 + 4p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 4p + 1 + p2 = 0 + 1 Reorder the terms: -1 + 1 + 4p + p2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4p + p2 = 0 + 1 4p + p2 = 0 + 1 Combine like terms: 0 + 1 = 1 4p + p2 = 1 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = 1 + 4 Reorder the terms: 4 + 4p + p2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + 4p + p2 = 5 Factor a perfect square on the left side: (p + 2)(p + 2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (p + 2) equal to 2.236067978 and -2.236067978.Subproblem 1
p + 2 = 2.236067978 Simplifying p + 2 = 2.236067978 Reorder the terms: 2 + p = 2.236067978 Solving 2 + p = 2.236067978 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + p = 2.236067978 + -2 p = 2.236067978 + -2 Combine like terms: 2.236067978 + -2 = 0.236067978 p = 0.236067978 Simplifying p = 0.236067978Subproblem 2
p + 2 = -2.236067978 Simplifying p + 2 = -2.236067978 Reorder the terms: 2 + p = -2.236067978 Solving 2 + p = -2.236067978 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = -2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + p = -2.236067978 + -2 p = -2.236067978 + -2 Combine like terms: -2.236067978 + -2 = -4.236067978 p = -4.236067978 Simplifying p = -4.236067978Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.236067978, -4.236067978}Solution
p = {0.236067978, -4.236067978}
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