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Simplifying p2 = 5 + 2p Solving p2 = 5 + 2p Solving for variable 'p'. Reorder the terms: -5 + -2p + p2 = 5 + 2p + -5 + -2p Reorder the terms: -5 + -2p + p2 = 5 + -5 + 2p + -2p Combine like terms: 5 + -5 = 0 -5 + -2p + p2 = 0 + 2p + -2p -5 + -2p + p2 = 2p + -2p Combine like terms: 2p + -2p = 0 -5 + -2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -2p + 5 + p2 = 0 + 5 Reorder the terms: -5 + 5 + -2p + p2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2p + p2 = 0 + 5 -2p + p2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2p + p2 = 5 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 = 5 + 1 Reorder the terms: 1 + -2p + p2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + -2p + p2 = 6 Factor a perfect square on the left side: (p + -1)(p + -1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (p + -1) equal to 2.449489743 and -2.449489743.Subproblem 1
p + -1 = 2.449489743 Simplifying p + -1 = 2.449489743 Reorder the terms: -1 + p = 2.449489743 Solving -1 + p = 2.449489743 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 = 2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + p = 2.449489743 + 1 p = 2.449489743 + 1 Combine like terms: 2.449489743 + 1 = 3.449489743 p = 3.449489743 Simplifying p = 3.449489743Subproblem 2
p + -1 = -2.449489743 Simplifying p + -1 = -2.449489743 Reorder the terms: -1 + p = -2.449489743 Solving -1 + p = -2.449489743 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 = -2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + p = -2.449489743 + 1 p = -2.449489743 + 1 Combine like terms: -2.449489743 + 1 = -1.449489743 p = -1.449489743 Simplifying p = -1.449489743Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.449489743, -1.449489743}
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