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Simplifying 4p2 + 13p = 2 + -4p2 + -2p Reorder the terms: 13p + 4p2 = 2 + -4p2 + -2p Reorder the terms: 13p + 4p2 = 2 + -2p + -4p2 Solving 13p + 4p2 = 2 + -2p + -4p2 Solving for variable 'p'. Reorder the terms: -2 + 13p + 2p + 4p2 + 4p2 = 2 + -2p + -4p2 + -2 + 2p + 4p2 Combine like terms: 13p + 2p = 15p -2 + 15p + 4p2 + 4p2 = 2 + -2p + -4p2 + -2 + 2p + 4p2 Combine like terms: 4p2 + 4p2 = 8p2 -2 + 15p + 8p2 = 2 + -2p + -4p2 + -2 + 2p + 4p2 Reorder the terms: -2 + 15p + 8p2 = 2 + -2 + -2p + 2p + -4p2 + 4p2 Combine like terms: 2 + -2 = 0 -2 + 15p + 8p2 = 0 + -2p + 2p + -4p2 + 4p2 -2 + 15p + 8p2 = -2p + 2p + -4p2 + 4p2 Combine like terms: -2p + 2p = 0 -2 + 15p + 8p2 = 0 + -4p2 + 4p2 -2 + 15p + 8p2 = -4p2 + 4p2 Combine like terms: -4p2 + 4p2 = 0 -2 + 15p + 8p2 = 0 Factor a trinomial. (-2 + -1p)(1 + -8p) = 0Subproblem 1
Set the factor '(-2 + -1p)' equal to zero and attempt to solve: Simplifying -2 + -1p = 0 Solving -2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1p = 0 + 2 -1p = 0 + 2 Combine like terms: 0 + 2 = 2 -1p = 2 Divide each side by '-1'. p = -2 Simplifying p = -2Subproblem 2
Set the factor '(1 + -8p)' equal to zero and attempt to solve: Simplifying 1 + -8p = 0 Solving 1 + -8p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -8p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8p = 0 + -1 -8p = 0 + -1 Combine like terms: 0 + -1 = -1 -8p = -1 Divide each side by '-8'. p = 0.125 Simplifying p = 0.125Solution
p = {-2, 0.125}
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