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Simplifying p2 + 20p = 27 Reorder the terms: 20p + p2 = 27 Solving 20p + p2 = 27 Solving for variable 'p'. Reorder the terms: -27 + 20p + p2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 20p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 20p + 27 + p2 = 0 + 27 Reorder the terms: -27 + 27 + 20p + p2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 20p + p2 = 0 + 27 20p + p2 = 0 + 27 Combine like terms: 0 + 27 = 27 20p + p2 = 27 The p term is 20p. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20p + 100 + p2 = 27 + 100 Reorder the terms: 100 + 20p + p2 = 27 + 100 Combine like terms: 27 + 100 = 127 100 + 20p + p2 = 127 Factor a perfect square on the left side: (p + 10)(p + 10) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (p + 10) equal to 11.26942767 and -11.26942767.Subproblem 1
p + 10 = 11.26942767 Simplifying p + 10 = 11.26942767 Reorder the terms: 10 + p = 11.26942767 Solving 10 + p = 11.26942767 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + p = 11.26942767 + -10 Combine like terms: 10 + -10 = 0 0 + p = 11.26942767 + -10 p = 11.26942767 + -10 Combine like terms: 11.26942767 + -10 = 1.26942767 p = 1.26942767 Simplifying p = 1.26942767Subproblem 2
p + 10 = -11.26942767 Simplifying p + 10 = -11.26942767 Reorder the terms: 10 + p = -11.26942767 Solving 10 + p = -11.26942767 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + p = -11.26942767 + -10 Combine like terms: 10 + -10 = 0 0 + p = -11.26942767 + -10 p = -11.26942767 + -10 Combine like terms: -11.26942767 + -10 = -21.26942767 p = -21.26942767 Simplifying p = -21.26942767Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.26942767, -21.26942767}
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