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Simplifying p2 + -1p * 4 = 63 Reorder the terms for easier multiplication: p2 + -1 * 4p = 63 Multiply -1 * 4 p2 + -4p = 63 Reorder the terms: -4p + p2 = 63 Solving -4p + p2 = 63 Solving for variable 'p'. Reorder the terms: -63 + -4p + p2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + -4p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + -4p + 63 + p2 = 0 + 63 Reorder the terms: -63 + 63 + -4p + p2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -4p + p2 = 0 + 63 -4p + p2 = 0 + 63 Combine like terms: 0 + 63 = 63 -4p + p2 = 63 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 = 63 + 4 Reorder the terms: 4 + -4p + p2 = 63 + 4 Combine like terms: 63 + 4 = 67 4 + -4p + p2 = 67 Factor a perfect square on the left side: (p + -2)(p + -2) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (p + -2) equal to 8.185352772 and -8.185352772.Subproblem 1
p + -2 = 8.185352772 Simplifying p + -2 = 8.185352772 Reorder the terms: -2 + p = 8.185352772 Solving -2 + p = 8.185352772 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 = 8.185352772 + 2 Combine like terms: -2 + 2 = 0 0 + p = 8.185352772 + 2 p = 8.185352772 + 2 Combine like terms: 8.185352772 + 2 = 10.185352772 p = 10.185352772 Simplifying p = 10.185352772Subproblem 2
p + -2 = -8.185352772 Simplifying p + -2 = -8.185352772 Reorder the terms: -2 + p = -8.185352772 Solving -2 + p = -8.185352772 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 = -8.185352772 + 2 Combine like terms: -2 + 2 = 0 0 + p = -8.185352772 + 2 p = -8.185352772 + 2 Combine like terms: -8.185352772 + 2 = -6.185352772 p = -6.185352772 Simplifying p = -6.185352772Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.185352772, -6.185352772}
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