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Simplifying 4p2 + 9 + -12p = 59 + -47p Reorder the terms: 9 + -12p + 4p2 = 59 + -47p Solving 9 + -12p + 4p2 = 59 + -47p Solving for variable 'p'. Reorder the terms: 9 + -59 + -12p + 47p + 4p2 = 59 + -47p + -59 + 47p Combine like terms: 9 + -59 = -50 -50 + -12p + 47p + 4p2 = 59 + -47p + -59 + 47p Combine like terms: -12p + 47p = 35p -50 + 35p + 4p2 = 59 + -47p + -59 + 47p Reorder the terms: -50 + 35p + 4p2 = 59 + -59 + -47p + 47p Combine like terms: 59 + -59 = 0 -50 + 35p + 4p2 = 0 + -47p + 47p -50 + 35p + 4p2 = -47p + 47p Combine like terms: -47p + 47p = 0 -50 + 35p + 4p2 = 0 Factor a trinomial. (-10 + -1p)(5 + -4p) = 0Subproblem 1
Set the factor '(-10 + -1p)' equal to zero and attempt to solve: Simplifying -10 + -1p = 0 Solving -10 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1p = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1p = 0 + 10 -1p = 0 + 10 Combine like terms: 0 + 10 = 10 -1p = 10 Divide each side by '-1'. p = -10 Simplifying p = -10Subproblem 2
Set the factor '(5 + -4p)' equal to zero and attempt to solve: Simplifying 5 + -4p = 0 Solving 5 + -4p = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4p = 0 + -5 -4p = 0 + -5 Combine like terms: 0 + -5 = -5 -4p = -5 Divide each side by '-4'. p = 1.25 Simplifying p = 1.25Solution
p = {-10, 1.25}
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