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Simplifying p2 + 6p + -18 = 0 Reorder the terms: -18 + 6p + p2 = 0 Solving -18 + 6p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 6p + 18 + p2 = 0 + 18 Reorder the terms: -18 + 18 + 6p + p2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 6p + p2 = 0 + 18 6p + p2 = 0 + 18 Combine like terms: 0 + 18 = 18 6p + p2 = 18 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 = 18 + 9 Reorder the terms: 9 + 6p + p2 = 18 + 9 Combine like terms: 18 + 9 = 27 9 + 6p + p2 = 27 Factor a perfect square on the left side: (p + 3)(p + 3) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (p + 3) equal to 5.196152423 and -5.196152423.Subproblem 1
p + 3 = 5.196152423 Simplifying p + 3 = 5.196152423 Reorder the terms: 3 + p = 5.196152423 Solving 3 + p = 5.196152423 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 = 5.196152423 + -3 Combine like terms: 3 + -3 = 0 0 + p = 5.196152423 + -3 p = 5.196152423 + -3 Combine like terms: 5.196152423 + -3 = 2.196152423 p = 2.196152423 Simplifying p = 2.196152423Subproblem 2
p + 3 = -5.196152423 Simplifying p + 3 = -5.196152423 Reorder the terms: 3 + p = -5.196152423 Solving 3 + p = -5.196152423 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 = -5.196152423 + -3 Combine like terms: 3 + -3 = 0 0 + p = -5.196152423 + -3 p = -5.196152423 + -3 Combine like terms: -5.196152423 + -3 = -8.196152423 p = -8.196152423 Simplifying p = -8.196152423Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.196152423, -8.196152423}
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