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Simplifying p = (p + -4)(160 + 8p) Reorder the terms: p = (-4 + p)(160 + 8p) Multiply (-4 + p) * (160 + 8p) p = (-4(160 + 8p) + p(160 + 8p)) p = ((160 * -4 + 8p * -4) + p(160 + 8p)) p = ((-640 + -32p) + p(160 + 8p)) p = (-640 + -32p + (160 * p + 8p * p)) p = (-640 + -32p + (160p + 8p2)) Combine like terms: -32p + 160p = 128p p = (-640 + 128p + 8p2) Solving p = -640 + 128p + 8p2 Solving for variable 'p'. Reorder the terms: 640 + p + -128p + -8p2 = -640 + 128p + 8p2 + 640 + -128p + -8p2 Combine like terms: p + -128p = -127p 640 + -127p + -8p2 = -640 + 128p + 8p2 + 640 + -128p + -8p2 Reorder the terms: 640 + -127p + -8p2 = -640 + 640 + 128p + -128p + 8p2 + -8p2 Combine like terms: -640 + 640 = 0 640 + -127p + -8p2 = 0 + 128p + -128p + 8p2 + -8p2 640 + -127p + -8p2 = 128p + -128p + 8p2 + -8p2 Combine like terms: 128p + -128p = 0 640 + -127p + -8p2 = 0 + 8p2 + -8p2 640 + -127p + -8p2 = 8p2 + -8p2 Combine like terms: 8p2 + -8p2 = 0 640 + -127p + -8p2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -80 + 15.875p + p2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 15.875p + 80 + p2 = 0 + 80 Reorder the terms: -80 + 80 + 15.875p + p2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 15.875p + p2 = 0 + 80 15.875p + p2 = 0 + 80 Combine like terms: 0 + 80 = 80 15.875p + p2 = 80 The p term is 15.875p. Take half its coefficient (7.9375). Square it (63.00390625) and add it to both sides. Add '63.00390625' to each side of the equation. 15.875p + 63.00390625 + p2 = 80 + 63.00390625 Reorder the terms: 63.00390625 + 15.875p + p2 = 80 + 63.00390625 Combine like terms: 80 + 63.00390625 = 143.00390625 63.00390625 + 15.875p + p2 = 143.00390625 Factor a perfect square on the left side: (p + 7.9375)(p + 7.9375) = 143.00390625 Calculate the square root of the right side: 11.958424071 Break this problem into two subproblems by setting (p + 7.9375) equal to 11.958424071 and -11.958424071.Subproblem 1
p + 7.9375 = 11.958424071 Simplifying p + 7.9375 = 11.958424071 Reorder the terms: 7.9375 + p = 11.958424071 Solving 7.9375 + p = 11.958424071 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7.9375' to each side of the equation. 7.9375 + -7.9375 + p = 11.958424071 + -7.9375 Combine like terms: 7.9375 + -7.9375 = 0.0000 0.0000 + p = 11.958424071 + -7.9375 p = 11.958424071 + -7.9375 Combine like terms: 11.958424071 + -7.9375 = 4.020924071 p = 4.020924071 Simplifying p = 4.020924071Subproblem 2
p + 7.9375 = -11.958424071 Simplifying p + 7.9375 = -11.958424071 Reorder the terms: 7.9375 + p = -11.958424071 Solving 7.9375 + p = -11.958424071 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7.9375' to each side of the equation. 7.9375 + -7.9375 + p = -11.958424071 + -7.9375 Combine like terms: 7.9375 + -7.9375 = 0.0000 0.0000 + p = -11.958424071 + -7.9375 p = -11.958424071 + -7.9375 Combine like terms: -11.958424071 + -7.9375 = -19.895924071 p = -19.895924071 Simplifying p = -19.895924071Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.020924071, -19.895924071}
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