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Simplifying 2p2 + 15p = 22 Reorder the terms: 15p + 2p2 = 22 Solving 15p + 2p2 = 22 Solving for variable 'p'. Reorder the terms: -22 + 15p + 2p2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + 15p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11 + 7.5p + p2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 7.5p + 11 + p2 = 0 + 11 Reorder the terms: -11 + 11 + 7.5p + p2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 7.5p + p2 = 0 + 11 7.5p + p2 = 0 + 11 Combine like terms: 0 + 11 = 11 7.5p + p2 = 11 The p term is 7.5p. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5p + 14.0625 + p2 = 11 + 14.0625 Reorder the terms: 14.0625 + 7.5p + p2 = 11 + 14.0625 Combine like terms: 11 + 14.0625 = 25.0625 14.0625 + 7.5p + p2 = 25.0625 Factor a perfect square on the left side: (p + 3.75)(p + 3.75) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (p + 3.75) equal to 5.006246099 and -5.006246099.Subproblem 1
p + 3.75 = 5.006246099 Simplifying p + 3.75 = 5.006246099 Reorder the terms: 3.75 + p = 5.006246099 Solving 3.75 + p = 5.006246099 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + p = 5.006246099 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + p = 5.006246099 + -3.75 p = 5.006246099 + -3.75 Combine like terms: 5.006246099 + -3.75 = 1.256246099 p = 1.256246099 Simplifying p = 1.256246099Subproblem 2
p + 3.75 = -5.006246099 Simplifying p + 3.75 = -5.006246099 Reorder the terms: 3.75 + p = -5.006246099 Solving 3.75 + p = -5.006246099 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + p = -5.006246099 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + p = -5.006246099 + -3.75 p = -5.006246099 + -3.75 Combine like terms: -5.006246099 + -3.75 = -8.756246099 p = -8.756246099 Simplifying p = -8.756246099Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.256246099, -8.756246099}
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