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Simplifying p2 + -1p = 27 Reorder the terms: -1p + p2 = 27 Solving -1p + p2 = 27 Solving for variable 'p'. Reorder the terms: -27 + -1p + p2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -1p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -1p + 27 + p2 = 0 + 27 Reorder the terms: -27 + 27 + -1p + p2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -1p + p2 = 0 + 27 -1p + p2 = 0 + 27 Combine like terms: 0 + 27 = 27 -1p + p2 = 27 The p term is -1p. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1p + 0.25 + p2 = 27 + 0.25 Reorder the terms: 0.25 + -1p + p2 = 27 + 0.25 Combine like terms: 27 + 0.25 = 27.25 0.25 + -1p + p2 = 27.25 Factor a perfect square on the left side: (p + -0.5)(p + -0.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (p + -0.5) equal to 5.220153254 and -5.220153254.Subproblem 1
p + -0.5 = 5.220153254 Simplifying p + -0.5 = 5.220153254 Reorder the terms: -0.5 + p = 5.220153254 Solving -0.5 + p = 5.220153254 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = 5.220153254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = 5.220153254 + 0.5 p = 5.220153254 + 0.5 Combine like terms: 5.220153254 + 0.5 = 5.720153254 p = 5.720153254 Simplifying p = 5.720153254Subproblem 2
p + -0.5 = -5.220153254 Simplifying p + -0.5 = -5.220153254 Reorder the terms: -0.5 + p = -5.220153254 Solving -0.5 + p = -5.220153254 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = -5.220153254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = -5.220153254 + 0.5 p = -5.220153254 + 0.5 Combine like terms: -5.220153254 + 0.5 = -4.720153254 p = -4.720153254 Simplifying p = -4.720153254Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.720153254, -4.720153254}
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