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Simplifying 5p2 + 10p + -236 = 0 Reorder the terms: -236 + 10p + 5p2 = 0 Solving -236 + 10p + 5p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -47.2 + 2p + p2 = 0 Move the constant term to the right: Add '47.2' to each side of the equation. -47.2 + 2p + 47.2 + p2 = 0 + 47.2 Reorder the terms: -47.2 + 47.2 + 2p + p2 = 0 + 47.2 Combine like terms: -47.2 + 47.2 = 0.0 0.0 + 2p + p2 = 0 + 47.2 2p + p2 = 0 + 47.2 Combine like terms: 0 + 47.2 = 47.2 2p + p2 = 47.2 The p term is 2p. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2p + 1 + p2 = 47.2 + 1 Reorder the terms: 1 + 2p + p2 = 47.2 + 1 Combine like terms: 47.2 + 1 = 48.2 1 + 2p + p2 = 48.2 Factor a perfect square on the left side: (p + 1)(p + 1) = 48.2 Calculate the square root of the right side: 6.942621983 Break this problem into two subproblems by setting (p + 1) equal to 6.942621983 and -6.942621983.Subproblem 1
p + 1 = 6.942621983 Simplifying p + 1 = 6.942621983 Reorder the terms: 1 + p = 6.942621983 Solving 1 + p = 6.942621983 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 6.942621983 + -1 Combine like terms: 1 + -1 = 0 0 + p = 6.942621983 + -1 p = 6.942621983 + -1 Combine like terms: 6.942621983 + -1 = 5.942621983 p = 5.942621983 Simplifying p = 5.942621983Subproblem 2
p + 1 = -6.942621983 Simplifying p + 1 = -6.942621983 Reorder the terms: 1 + p = -6.942621983 Solving 1 + p = -6.942621983 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = -6.942621983 + -1 Combine like terms: 1 + -1 = 0 0 + p = -6.942621983 + -1 p = -6.942621983 + -1 Combine like terms: -6.942621983 + -1 = -7.942621983 p = -7.942621983 Simplifying p = -7.942621983Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.942621983, -7.942621983}
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