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Simplifying 31P = 4P2 + 21 Reorder the terms: 31P = 21 + 4P2 Solving 31P = 21 + 4P2 Solving for variable 'P'. Reorder the terms: -21 + 31P + -4P2 = 21 + 4P2 + -21 + -4P2 Reorder the terms: -21 + 31P + -4P2 = 21 + -21 + 4P2 + -4P2 Combine like terms: 21 + -21 = 0 -21 + 31P + -4P2 = 0 + 4P2 + -4P2 -21 + 31P + -4P2 = 4P2 + -4P2 Combine like terms: 4P2 + -4P2 = 0 -21 + 31P + -4P2 = 0 Factor a trinomial. (-7 + P)(3 + -4P) = 0Subproblem 1
Set the factor '(-7 + P)' equal to zero and attempt to solve: Simplifying -7 + P = 0 Solving -7 + P = 0 Move all terms containing P to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + P = 0 + 7 Combine like terms: -7 + 7 = 0 0 + P = 0 + 7 P = 0 + 7 Combine like terms: 0 + 7 = 7 P = 7 Simplifying P = 7Subproblem 2
Set the factor '(3 + -4P)' equal to zero and attempt to solve: Simplifying 3 + -4P = 0 Solving 3 + -4P = 0 Move all terms containing P to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4P = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4P = 0 + -3 -4P = 0 + -3 Combine like terms: 0 + -3 = -3 -4P = -3 Divide each side by '-4'. P = 0.75 Simplifying P = 0.75Solution
P = {7, 0.75}
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