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Simplifying p2 + -1 = -2p Reorder the terms: -1 + p2 = -2p Solving -1 + p2 = -2p Solving for variable 'p'. Reorder the terms: -1 + 2p + p2 = -2p + 2p Combine like terms: -2p + 2p = 0 -1 + 2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 2p + 1 + p2 = 0 + 1 Reorder the terms: -1 + 1 + 2p + p2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2p + p2 = 0 + 1 2p + p2 = 0 + 1 Combine like terms: 0 + 1 = 1 2p + p2 = 1 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 = 1 + 1 Reorder the terms: 1 + 2p + p2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + 2p + p2 = 2 Factor a perfect square on the left side: (p + 1)(p + 1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (p + 1) equal to 1.414213562 and -1.414213562.Subproblem 1
p + 1 = 1.414213562 Simplifying p + 1 = 1.414213562 Reorder the terms: 1 + p = 1.414213562 Solving 1 + p = 1.414213562 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 = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + p = 1.414213562 + -1 p = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 p = 0.414213562 Simplifying p = 0.414213562Subproblem 2
p + 1 = -1.414213562 Simplifying p + 1 = -1.414213562 Reorder the terms: 1 + p = -1.414213562 Solving 1 + p = -1.414213562 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 = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + p = -1.414213562 + -1 p = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 p = -2.414213562 Simplifying p = -2.414213562Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.414213562, -2.414213562}
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