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Simplifying 24 + -3P2 + 20P = 0 Reorder the terms: 24 + 20P + -3P2 = 0 Solving 24 + 20P + -3P2 = 0 Solving for variable 'P'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -8 + -6.666666667P + P2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -6.666666667P + 8 + P2 = 0 + 8 Reorder the terms: -8 + 8 + -6.666666667P + P2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6.666666667P + P2 = 0 + 8 -6.666666667P + P2 = 0 + 8 Combine like terms: 0 + 8 = 8 -6.666666667P + P2 = 8 The P term is -6.666666667P. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667P + 11.11111112 + P2 = 8 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667P + P2 = 8 + 11.11111112 Combine like terms: 8 + 11.11111112 = 19.11111112 11.11111112 + -6.666666667P + P2 = 19.11111112 Factor a perfect square on the left side: (P + -3.333333334)(P + -3.333333334) = 19.11111112 Calculate the square root of the right side: 4.371625684 Break this problem into two subproblems by setting (P + -3.333333334) equal to 4.371625684 and -4.371625684.Subproblem 1
P + -3.333333334 = 4.371625684 Simplifying P + -3.333333334 = 4.371625684 Reorder the terms: -3.333333334 + P = 4.371625684 Solving -3.333333334 + P = 4.371625684 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + P = 4.371625684 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + P = 4.371625684 + 3.333333334 P = 4.371625684 + 3.333333334 Combine like terms: 4.371625684 + 3.333333334 = 7.704959018 P = 7.704959018 Simplifying P = 7.704959018Subproblem 2
P + -3.333333334 = -4.371625684 Simplifying P + -3.333333334 = -4.371625684 Reorder the terms: -3.333333334 + P = -4.371625684 Solving -3.333333334 + P = -4.371625684 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + P = -4.371625684 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + P = -4.371625684 + 3.333333334 P = -4.371625684 + 3.333333334 Combine like terms: -4.371625684 + 3.333333334 = -1.03829235 P = -1.03829235 Simplifying P = -1.03829235Solution
The solution to the problem is based on the solutions from the subproblems. P = {7.704959018, -1.03829235}
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