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Simplifying p2 + 9p + 12 = 0 Reorder the terms: 12 + 9p + p2 = 0 Solving 12 + 9p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 9p + -12 + p2 = 0 + -12 Reorder the terms: 12 + -12 + 9p + p2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 9p + p2 = 0 + -12 9p + p2 = 0 + -12 Combine like terms: 0 + -12 = -12 9p + p2 = -12 The p term is 9p. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9p + 20.25 + p2 = -12 + 20.25 Reorder the terms: 20.25 + 9p + p2 = -12 + 20.25 Combine like terms: -12 + 20.25 = 8.25 20.25 + 9p + p2 = 8.25 Factor a perfect square on the left side: (p + 4.5)(p + 4.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (p + 4.5) equal to 2.872281323 and -2.872281323.Subproblem 1
p + 4.5 = 2.872281323 Simplifying p + 4.5 = 2.872281323 Reorder the terms: 4.5 + p = 2.872281323 Solving 4.5 + p = 2.872281323 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + p = 2.872281323 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = 2.872281323 + -4.5 p = 2.872281323 + -4.5 Combine like terms: 2.872281323 + -4.5 = -1.627718677 p = -1.627718677 Simplifying p = -1.627718677Subproblem 2
p + 4.5 = -2.872281323 Simplifying p + 4.5 = -2.872281323 Reorder the terms: 4.5 + p = -2.872281323 Solving 4.5 + p = -2.872281323 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + p = -2.872281323 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = -2.872281323 + -4.5 p = -2.872281323 + -4.5 Combine like terms: -2.872281323 + -4.5 = -7.372281323 p = -7.372281323 Simplifying p = -7.372281323Solution
The solution to the problem is based on the solutions from the subproblems. p = {-1.627718677, -7.372281323}
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