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Simplifying 3p2 + -15p + 11 = 0 Reorder the terms: 11 + -15p + 3p2 = 0 Solving 11 + -15p + 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'. 3.666666667 + -5p + p2 = 0 Move the constant term to the right: Add '-3.666666667' to each side of the equation. 3.666666667 + -5p + -3.666666667 + p2 = 0 + -3.666666667 Reorder the terms: 3.666666667 + -3.666666667 + -5p + p2 = 0 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + -5p + p2 = 0 + -3.666666667 -5p + p2 = 0 + -3.666666667 Combine like terms: 0 + -3.666666667 = -3.666666667 -5p + p2 = -3.666666667 The p term is -5p. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5p + 6.25 + p2 = -3.666666667 + 6.25 Reorder the terms: 6.25 + -5p + p2 = -3.666666667 + 6.25 Combine like terms: -3.666666667 + 6.25 = 2.583333333 6.25 + -5p + p2 = 2.583333333 Factor a perfect square on the left side: (p + -2.5)(p + -2.5) = 2.583333333 Calculate the square root of the right side: 1.607275127 Break this problem into two subproblems by setting (p + -2.5) equal to 1.607275127 and -1.607275127.Subproblem 1
p + -2.5 = 1.607275127 Simplifying p + -2.5 = 1.607275127 Reorder the terms: -2.5 + p = 1.607275127 Solving -2.5 + p = 1.607275127 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + p = 1.607275127 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = 1.607275127 + 2.5 p = 1.607275127 + 2.5 Combine like terms: 1.607275127 + 2.5 = 4.107275127 p = 4.107275127 Simplifying p = 4.107275127Subproblem 2
p + -2.5 = -1.607275127 Simplifying p + -2.5 = -1.607275127 Reorder the terms: -2.5 + p = -1.607275127 Solving -2.5 + p = -1.607275127 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + p = -1.607275127 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = -1.607275127 + 2.5 p = -1.607275127 + 2.5 Combine like terms: -1.607275127 + 2.5 = 0.892724873 p = 0.892724873 Simplifying p = 0.892724873Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.107275127, 0.892724873}
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