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Simplifying (p2 + 6p + -20) = 0 Reorder the terms: (-20 + 6p + p2) = 0 Remove parenthesis around (-20 + 6p + p2) -20 + 6p + p2 = 0 Solving -20 + 6p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 6p + 20 + p2 = 0 + 20 Reorder the terms: -20 + 20 + 6p + p2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 6p + p2 = 0 + 20 6p + p2 = 0 + 20 Combine like terms: 0 + 20 = 20 6p + p2 = 20 The p term is 6p. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6p + 9 + p2 = 20 + 9 Reorder the terms: 9 + 6p + p2 = 20 + 9 Combine like terms: 20 + 9 = 29 9 + 6p + p2 = 29 Factor a perfect square on the left side: (p + 3)(p + 3) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (p + 3) equal to 5.385164807 and -5.385164807.Subproblem 1
p + 3 = 5.385164807 Simplifying p + 3 = 5.385164807 Reorder the terms: 3 + p = 5.385164807 Solving 3 + p = 5.385164807 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 5.385164807 + -3 Combine like terms: 3 + -3 = 0 0 + p = 5.385164807 + -3 p = 5.385164807 + -3 Combine like terms: 5.385164807 + -3 = 2.385164807 p = 2.385164807 Simplifying p = 2.385164807Subproblem 2
p + 3 = -5.385164807 Simplifying p + 3 = -5.385164807 Reorder the terms: 3 + p = -5.385164807 Solving 3 + p = -5.385164807 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = -5.385164807 + -3 Combine like terms: 3 + -3 = 0 0 + p = -5.385164807 + -3 p = -5.385164807 + -3 Combine like terms: -5.385164807 + -3 = -8.385164807 p = -8.385164807 Simplifying p = -8.385164807Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.385164807, -8.385164807}
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