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Simplifying p2 + 8p = 13 Reorder the terms: 8p + p2 = 13 Solving 8p + p2 = 13 Solving for variable 'p'. Reorder the terms: -13 + 8p + p2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 8p + 13 + p2 = 0 + 13 Reorder the terms: -13 + 13 + 8p + p2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 8p + p2 = 0 + 13 8p + p2 = 0 + 13 Combine like terms: 0 + 13 = 13 8p + p2 = 13 The p term is 8p. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8p + 16 + p2 = 13 + 16 Reorder the terms: 16 + 8p + p2 = 13 + 16 Combine like terms: 13 + 16 = 29 16 + 8p + p2 = 29 Factor a perfect square on the left side: (p + 4)(p + 4) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (p + 4) equal to 5.385164807 and -5.385164807.Subproblem 1
p + 4 = 5.385164807 Simplifying p + 4 = 5.385164807 Reorder the terms: 4 + p = 5.385164807 Solving 4 + p = 5.385164807 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = 5.385164807 + -4 Combine like terms: 4 + -4 = 0 0 + p = 5.385164807 + -4 p = 5.385164807 + -4 Combine like terms: 5.385164807 + -4 = 1.385164807 p = 1.385164807 Simplifying p = 1.385164807Subproblem 2
p + 4 = -5.385164807 Simplifying p + 4 = -5.385164807 Reorder the terms: 4 + p = -5.385164807 Solving 4 + p = -5.385164807 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = -5.385164807 + -4 Combine like terms: 4 + -4 = 0 0 + p = -5.385164807 + -4 p = -5.385164807 + -4 Combine like terms: -5.385164807 + -4 = -9.385164807 p = -9.385164807 Simplifying p = -9.385164807Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.385164807, -9.385164807}
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