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Simplifying -11.5(9.5 + 6.4p) + 1.9p(7.1p + -5.552) = 0 (9.5 * -11.5 + 6.4p * -11.5) + 1.9p(7.1p + -5.552) = 0 (-109.25 + -73.6p) + 1.9p(7.1p + -5.552) = 0 Reorder the terms: -109.25 + -73.6p + 1.9p(-5.552 + 7.1p) = 0 -109.25 + -73.6p + (-5.552 * 1.9p + 7.1p * 1.9p) = 0 -109.25 + -73.6p + (-10.5488p + 13.49p2) = 0 Combine like terms: -73.6p + -10.5488p = -84.1488p -109.25 + -84.1488p + 13.49p2 = 0 Solving -109.25 + -84.1488p + 13.49p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 13.49 the coefficient of the squared term: Divide each side by '13.49'. -8.098591549 + -6.237865085p + p2 = 0 Move the constant term to the right: Add '8.098591549' to each side of the equation. -8.098591549 + -6.237865085p + 8.098591549 + p2 = 0 + 8.098591549 Reorder the terms: -8.098591549 + 8.098591549 + -6.237865085p + p2 = 0 + 8.098591549 Combine like terms: -8.098591549 + 8.098591549 = 0.000000000 0.000000000 + -6.237865085p + p2 = 0 + 8.098591549 -6.237865085p + p2 = 0 + 8.098591549 Combine like terms: 0 + 8.098591549 = 8.098591549 -6.237865085p + p2 = 8.098591549 The p term is -6.237865085p. Take half its coefficient (-3.118932543). Square it (9.727740208) and add it to both sides. Add '9.727740208' to each side of the equation. -6.237865085p + 9.727740208 + p2 = 8.098591549 + 9.727740208 Reorder the terms: 9.727740208 + -6.237865085p + p2 = 8.098591549 + 9.727740208 Combine like terms: 8.098591549 + 9.727740208 = 17.826331757 9.727740208 + -6.237865085p + p2 = 17.826331757 Factor a perfect square on the left side: (p + -3.118932543)(p + -3.118932543) = 17.826331757 Calculate the square root of the right side: 4.222124081 Break this problem into two subproblems by setting (p + -3.118932543) equal to 4.222124081 and -4.222124081.Subproblem 1
p + -3.118932543 = 4.222124081 Simplifying p + -3.118932543 = 4.222124081 Reorder the terms: -3.118932543 + p = 4.222124081 Solving -3.118932543 + p = 4.222124081 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.118932543' to each side of the equation. -3.118932543 + 3.118932543 + p = 4.222124081 + 3.118932543 Combine like terms: -3.118932543 + 3.118932543 = 0.000000000 0.000000000 + p = 4.222124081 + 3.118932543 p = 4.222124081 + 3.118932543 Combine like terms: 4.222124081 + 3.118932543 = 7.341056624 p = 7.341056624 Simplifying p = 7.341056624Subproblem 2
p + -3.118932543 = -4.222124081 Simplifying p + -3.118932543 = -4.222124081 Reorder the terms: -3.118932543 + p = -4.222124081 Solving -3.118932543 + p = -4.222124081 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.118932543' to each side of the equation. -3.118932543 + 3.118932543 + p = -4.222124081 + 3.118932543 Combine like terms: -3.118932543 + 3.118932543 = 0.000000000 0.000000000 + p = -4.222124081 + 3.118932543 p = -4.222124081 + 3.118932543 Combine like terms: -4.222124081 + 3.118932543 = -1.103191538 p = -1.103191538 Simplifying p = -1.103191538Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.341056624, -1.103191538}
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