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Simplifying 3p2 + -9p + -1 = 0 Reorder the terms: -1 + -9p + 3p2 = 0 Solving -1 + -9p + 3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + -3p + p2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -3p + 0.3333333333 + p2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -3p + p2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -3p + p2 = 0 + 0.3333333333 -3p + p2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -3p + p2 = 0.3333333333 The p term is -3p. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3p + 2.25 + p2 = 0.3333333333 + 2.25 Reorder the terms: 2.25 + -3p + p2 = 0.3333333333 + 2.25 Combine like terms: 0.3333333333 + 2.25 = 2.5833333333 2.25 + -3p + p2 = 2.5833333333 Factor a perfect square on the left side: (p + -1.5)(p + -1.5) = 2.5833333333 Calculate the square root of the right side: 1.607275127 Break this problem into two subproblems by setting (p + -1.5) equal to 1.607275127 and -1.607275127.Subproblem 1
p + -1.5 = 1.607275127 Simplifying p + -1.5 = 1.607275127 Reorder the terms: -1.5 + p = 1.607275127 Solving -1.5 + p = 1.607275127 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = 1.607275127 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = 1.607275127 + 1.5 p = 1.607275127 + 1.5 Combine like terms: 1.607275127 + 1.5 = 3.107275127 p = 3.107275127 Simplifying p = 3.107275127Subproblem 2
p + -1.5 = -1.607275127 Simplifying p + -1.5 = -1.607275127 Reorder the terms: -1.5 + p = -1.607275127 Solving -1.5 + p = -1.607275127 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = -1.607275127 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = -1.607275127 + 1.5 p = -1.607275127 + 1.5 Combine like terms: -1.607275127 + 1.5 = -0.107275127 p = -0.107275127 Simplifying p = -0.107275127Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.107275127, -0.107275127}
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