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Simplifying 2p2 = -21p + -41 Reorder the terms: 2p2 = -41 + -21p Solving 2p2 = -41 + -21p Solving for variable 'p'. Reorder the terms: 41 + 21p + 2p2 = -41 + -21p + 41 + 21p Reorder the terms: 41 + 21p + 2p2 = -41 + 41 + -21p + 21p Combine like terms: -41 + 41 = 0 41 + 21p + 2p2 = 0 + -21p + 21p 41 + 21p + 2p2 = -21p + 21p Combine like terms: -21p + 21p = 0 41 + 21p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 20.5 + 10.5p + p2 = 0 Move the constant term to the right: Add '-20.5' to each side of the equation. 20.5 + 10.5p + -20.5 + p2 = 0 + -20.5 Reorder the terms: 20.5 + -20.5 + 10.5p + p2 = 0 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + 10.5p + p2 = 0 + -20.5 10.5p + p2 = 0 + -20.5 Combine like terms: 0 + -20.5 = -20.5 10.5p + p2 = -20.5 The p term is 10.5p. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5p + 27.5625 + p2 = -20.5 + 27.5625 Reorder the terms: 27.5625 + 10.5p + p2 = -20.5 + 27.5625 Combine like terms: -20.5 + 27.5625 = 7.0625 27.5625 + 10.5p + p2 = 7.0625 Factor a perfect square on the left side: (p + 5.25)(p + 5.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (p + 5.25) equal to 2.657536453 and -2.657536453.Subproblem 1
p + 5.25 = 2.657536453 Simplifying p + 5.25 = 2.657536453 Reorder the terms: 5.25 + p = 2.657536453 Solving 5.25 + p = 2.657536453 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + p = 2.657536453 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + p = 2.657536453 + -5.25 p = 2.657536453 + -5.25 Combine like terms: 2.657536453 + -5.25 = -2.592463547 p = -2.592463547 Simplifying p = -2.592463547Subproblem 2
p + 5.25 = -2.657536453 Simplifying p + 5.25 = -2.657536453 Reorder the terms: 5.25 + p = -2.657536453 Solving 5.25 + p = -2.657536453 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + p = -2.657536453 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + p = -2.657536453 + -5.25 p = -2.657536453 + -5.25 Combine like terms: -2.657536453 + -5.25 = -7.907536453 p = -7.907536453 Simplifying p = -7.907536453Solution
The solution to the problem is based on the solutions from the subproblems. p = {-2.592463547, -7.907536453}
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