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Simplifying 2p2 + -10p + -15 = 0 Reorder the terms: -15 + -10p + 2p2 = 0 Solving -15 + -10p + 2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -5p + p2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -5p + 7.5 + p2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -5p + p2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -5p + p2 = 0 + 7.5 -5p + p2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -5p + p2 = 7.5 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 = 7.5 + 6.25 Reorder the terms: 6.25 + -5p + p2 = 7.5 + 6.25 Combine like terms: 7.5 + 6.25 = 13.75 6.25 + -5p + p2 = 13.75 Factor a perfect square on the left side: (p + -2.5)(p + -2.5) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (p + -2.5) equal to 3.708099244 and -3.708099244.Subproblem 1
p + -2.5 = 3.708099244 Simplifying p + -2.5 = 3.708099244 Reorder the terms: -2.5 + p = 3.708099244 Solving -2.5 + p = 3.708099244 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 = 3.708099244 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = 3.708099244 + 2.5 p = 3.708099244 + 2.5 Combine like terms: 3.708099244 + 2.5 = 6.208099244 p = 6.208099244 Simplifying p = 6.208099244Subproblem 2
p + -2.5 = -3.708099244 Simplifying p + -2.5 = -3.708099244 Reorder the terms: -2.5 + p = -3.708099244 Solving -2.5 + p = -3.708099244 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 = -3.708099244 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = -3.708099244 + 2.5 p = -3.708099244 + 2.5 Combine like terms: -3.708099244 + 2.5 = -1.208099244 p = -1.208099244 Simplifying p = -1.208099244Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.208099244, -1.208099244}
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