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Simplifying (2 * 4p) + -1(4p2) + 5 = 0 Multiply 2 * 4 (8p) + -1(4p2) + 5 = 0 Remove parenthesis around (4p2) (8p) + -1 * 4p2 + 5 = 0 Multiply -1 * 4 (8p) + -4p2 + 5 = 0 Reorder the terms: 5 + (8p) + -4p2 = 0 Solving 5 + (8p) + -4p2 = 0 Solving for variable 'p'. Factor a trinomial. (5 + -2p)(1 + 2p) = 0Subproblem 1
Set the factor '(5 + -2p)' equal to zero and attempt to solve: Simplifying 5 + -2p = 0 Solving 5 + -2p = 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 + -2p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2p = 0 + -5 -2p = 0 + -5 Combine like terms: 0 + -5 = -5 -2p = -5 Divide each side by '-2'. p = 2.5 Simplifying p = 2.5Subproblem 2
Set the factor '(1 + 2p)' equal to zero and attempt to solve: Simplifying 1 + 2p = 0 Solving 1 + 2p = 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 + 2p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2p = 0 + -1 2p = 0 + -1 Combine like terms: 0 + -1 = -1 2p = -1 Divide each side by '2'. p = -0.5 Simplifying p = -0.5Solution
p = {2.5, -0.5}
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