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Simplifying 3p + -4 + -6 = -2p(p + -5) Reorder the terms: -4 + -6 + 3p = -2p(p + -5) Combine like terms: -4 + -6 = -10 -10 + 3p = -2p(p + -5) Reorder the terms: -10 + 3p = -2p(-5 + p) -10 + 3p = (-5 * -2p + p * -2p) -10 + 3p = (10p + -2p2) Solving -10 + 3p = 10p + -2p2 Solving for variable 'p'. Combine like terms: 3p + -10p = -7p -10 + -7p + 2p2 = 10p + -2p2 + -10p + 2p2 Reorder the terms: -10 + -7p + 2p2 = 10p + -10p + -2p2 + 2p2 Combine like terms: 10p + -10p = 0 -10 + -7p + 2p2 = 0 + -2p2 + 2p2 -10 + -7p + 2p2 = -2p2 + 2p2 Combine like terms: -2p2 + 2p2 = 0 -10 + -7p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + -3.5p + p2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -3.5p + 5 + p2 = 0 + 5 Reorder the terms: -5 + 5 + -3.5p + p2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3.5p + p2 = 0 + 5 -3.5p + p2 = 0 + 5 Combine like terms: 0 + 5 = 5 -3.5p + p2 = 5 The p term is -3.5p. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5p + 3.0625 + p2 = 5 + 3.0625 Reorder the terms: 3.0625 + -3.5p + p2 = 5 + 3.0625 Combine like terms: 5 + 3.0625 = 8.0625 3.0625 + -3.5p + p2 = 8.0625 Factor a perfect square on the left side: (p + -1.75)(p + -1.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (p + -1.75) equal to 2.839454173 and -2.839454173.Subproblem 1
p + -1.75 = 2.839454173 Simplifying p + -1.75 = 2.839454173 Reorder the terms: -1.75 + p = 2.839454173 Solving -1.75 + p = 2.839454173 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + p = 2.839454173 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + p = 2.839454173 + 1.75 p = 2.839454173 + 1.75 Combine like terms: 2.839454173 + 1.75 = 4.589454173 p = 4.589454173 Simplifying p = 4.589454173Subproblem 2
p + -1.75 = -2.839454173 Simplifying p + -1.75 = -2.839454173 Reorder the terms: -1.75 + p = -2.839454173 Solving -1.75 + p = -2.839454173 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + p = -2.839454173 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + p = -2.839454173 + 1.75 p = -2.839454173 + 1.75 Combine like terms: -2.839454173 + 1.75 = -1.089454173 p = -1.089454173 Simplifying p = -1.089454173Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.589454173, -1.089454173}
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