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Simplifying (p + -1)(2p + 4) = 9 Reorder the terms: (-1 + p)(2p + 4) = 9 Reorder the terms: (-1 + p)(4 + 2p) = 9 Multiply (-1 + p) * (4 + 2p) (-1(4 + 2p) + p(4 + 2p)) = 9 ((4 * -1 + 2p * -1) + p(4 + 2p)) = 9 ((-4 + -2p) + p(4 + 2p)) = 9 (-4 + -2p + (4 * p + 2p * p)) = 9 (-4 + -2p + (4p + 2p2)) = 9 Combine like terms: -2p + 4p = 2p (-4 + 2p + 2p2) = 9 Solving -4 + 2p + 2p2 = 9 Solving for variable 'p'. Reorder the terms: -4 + -9 + 2p + 2p2 = 9 + -9 Combine like terms: -4 + -9 = -13 -13 + 2p + 2p2 = 9 + -9 Combine like terms: 9 + -9 = 0 -13 + 2p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + p + p2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + p + 6.5 + p2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + p + p2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + p + p2 = 0 + 6.5 p + p2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 p + p2 = 6.5 The p term is p. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + p2 = 6.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + p2 = 6.5 + 0.25 Combine like terms: 6.5 + 0.25 = 6.75 1.25 + p2 = 6.75 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (p + 0.5) equal to 2.598076211 and -2.598076211.Subproblem 1
p + 0.5 = 2.598076211 Simplifying p + 0.5 = 2.598076211 Reorder the terms: 0.5 + p = 2.598076211 Solving 0.5 + p = 2.598076211 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = 2.598076211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 2.598076211 + -0.5 p = 2.598076211 + -0.5 Combine like terms: 2.598076211 + -0.5 = 2.098076211 p = 2.098076211 Simplifying p = 2.098076211Subproblem 2
p + 0.5 = -2.598076211 Simplifying p + 0.5 = -2.598076211 Reorder the terms: 0.5 + p = -2.598076211 Solving 0.5 + p = -2.598076211 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = -2.598076211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -2.598076211 + -0.5 p = -2.598076211 + -0.5 Combine like terms: -2.598076211 + -0.5 = -3.098076211 p = -3.098076211 Simplifying p = -3.098076211Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.098076211, -3.098076211}
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