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Simplifying p2 + -2p + -47 = 0 Reorder the terms: -47 + -2p + p2 = 0 Solving -47 + -2p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -2p + 47 + p2 = 0 + 47 Reorder the terms: -47 + 47 + -2p + p2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -2p + p2 = 0 + 47 -2p + p2 = 0 + 47 Combine like terms: 0 + 47 = 47 -2p + p2 = 47 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 = 47 + 1 Reorder the terms: 1 + -2p + p2 = 47 + 1 Combine like terms: 47 + 1 = 48 1 + -2p + p2 = 48 Factor a perfect square on the left side: (p + -1)(p + -1) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (p + -1) equal to 6.92820323 and -6.92820323.Subproblem 1
p + -1 = 6.92820323 Simplifying p + -1 = 6.92820323 Reorder the terms: -1 + p = 6.92820323 Solving -1 + p = 6.92820323 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 = 6.92820323 + 1 Combine like terms: -1 + 1 = 0 0 + p = 6.92820323 + 1 p = 6.92820323 + 1 Combine like terms: 6.92820323 + 1 = 7.92820323 p = 7.92820323 Simplifying p = 7.92820323Subproblem 2
p + -1 = -6.92820323 Simplifying p + -1 = -6.92820323 Reorder the terms: -1 + p = -6.92820323 Solving -1 + p = -6.92820323 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 = -6.92820323 + 1 Combine like terms: -1 + 1 = 0 0 + p = -6.92820323 + 1 p = -6.92820323 + 1 Combine like terms: -6.92820323 + 1 = -5.92820323 p = -5.92820323 Simplifying p = -5.92820323Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.92820323, -5.92820323}
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