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Simplifying 6p2 + -85p + -160 = 0 Reorder the terms: -160 + -85p + 6p2 = 0 Solving -160 + -85p + 6p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -26.66666667 + -14.16666667p + p2 = 0 Move the constant term to the right: Add '26.66666667' to each side of the equation. -26.66666667 + -14.16666667p + 26.66666667 + p2 = 0 + 26.66666667 Reorder the terms: -26.66666667 + 26.66666667 + -14.16666667p + p2 = 0 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + -14.16666667p + p2 = 0 + 26.66666667 -14.16666667p + p2 = 0 + 26.66666667 Combine like terms: 0 + 26.66666667 = 26.66666667 -14.16666667p + p2 = 26.66666667 The p term is -14.16666667p. Take half its coefficient (-7.083333335). Square it (50.17361113) and add it to both sides. Add '50.17361113' to each side of the equation. -14.16666667p + 50.17361113 + p2 = 26.66666667 + 50.17361113 Reorder the terms: 50.17361113 + -14.16666667p + p2 = 26.66666667 + 50.17361113 Combine like terms: 26.66666667 + 50.17361113 = 76.8402778 50.17361113 + -14.16666667p + p2 = 76.8402778 Factor a perfect square on the left side: (p + -7.083333335)(p + -7.083333335) = 76.8402778 Calculate the square root of the right side: 8.765858646 Break this problem into two subproblems by setting (p + -7.083333335) equal to 8.765858646 and -8.765858646.Subproblem 1
p + -7.083333335 = 8.765858646 Simplifying p + -7.083333335 = 8.765858646 Reorder the terms: -7.083333335 + p = 8.765858646 Solving -7.083333335 + p = 8.765858646 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.083333335' to each side of the equation. -7.083333335 + 7.083333335 + p = 8.765858646 + 7.083333335 Combine like terms: -7.083333335 + 7.083333335 = 0.000000000 0.000000000 + p = 8.765858646 + 7.083333335 p = 8.765858646 + 7.083333335 Combine like terms: 8.765858646 + 7.083333335 = 15.849191981 p = 15.849191981 Simplifying p = 15.849191981Subproblem 2
p + -7.083333335 = -8.765858646 Simplifying p + -7.083333335 = -8.765858646 Reorder the terms: -7.083333335 + p = -8.765858646 Solving -7.083333335 + p = -8.765858646 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.083333335' to each side of the equation. -7.083333335 + 7.083333335 + p = -8.765858646 + 7.083333335 Combine like terms: -7.083333335 + 7.083333335 = 0.000000000 0.000000000 + p = -8.765858646 + 7.083333335 p = -8.765858646 + 7.083333335 Combine like terms: -8.765858646 + 7.083333335 = -1.682525311 p = -1.682525311 Simplifying p = -1.682525311Solution
The solution to the problem is based on the solutions from the subproblems. p = {15.849191981, -1.682525311}
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