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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 = 13p -10 + 13p + -2p2 = -10p + 2p2 + 10p + -2p2 Reorder the terms: -10 + 13p + -2p2 = -10p + 10p + 2p2 + -2p2 Combine like terms: -10p + 10p = 0 -10 + 13p + -2p2 = 0 + 2p2 + -2p2 -10 + 13p + -2p2 = 2p2 + -2p2 Combine like terms: 2p2 + -2p2 = 0 -10 + 13p + -2p2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 5 + -6.5p + p2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -6.5p + -5 + p2 = 0 + -5 Reorder the terms: 5 + -5 + -6.5p + p2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6.5p + p2 = 0 + -5 -6.5p + p2 = 0 + -5 Combine like terms: 0 + -5 = -5 -6.5p + p2 = -5 The p term is -6.5p. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5p + 10.5625 + p2 = -5 + 10.5625 Reorder the terms: 10.5625 + -6.5p + p2 = -5 + 10.5625 Combine like terms: -5 + 10.5625 = 5.5625 10.5625 + -6.5p + p2 = 5.5625 Factor a perfect square on the left side: (p + -3.25)(p + -3.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (p + -3.25) equal to 2.358495283 and -2.358495283.Subproblem 1
p + -3.25 = 2.358495283 Simplifying p + -3.25 = 2.358495283 Reorder the terms: -3.25 + p = 2.358495283 Solving -3.25 + p = 2.358495283 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + p = 2.358495283 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + p = 2.358495283 + 3.25 p = 2.358495283 + 3.25 Combine like terms: 2.358495283 + 3.25 = 5.608495283 p = 5.608495283 Simplifying p = 5.608495283Subproblem 2
p + -3.25 = -2.358495283 Simplifying p + -3.25 = -2.358495283 Reorder the terms: -3.25 + p = -2.358495283 Solving -3.25 + p = -2.358495283 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + p = -2.358495283 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + p = -2.358495283 + 3.25 p = -2.358495283 + 3.25 Combine like terms: -2.358495283 + 3.25 = 0.891504717 p = 0.891504717 Simplifying p = 0.891504717Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.608495283, 0.891504717}
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