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Simplifying (8p2) + -1(-16p) = 10 Remove parenthesis around (-16p) (8p2) + -1 * -16p = 10 Multiply -1 * -16 (8p2) + 16p = 10 Reorder the terms: 16p + (8p2) = 10 Solving 16p + (8p2) = 10 Solving for variable 'p'. Reorder the terms: -10 + 16p + (8p2) = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 16p + (8p2) = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 8p + (4p2)) = 0 Factor a trinomial. 2((-5 + -2p)(1 + -2p)) = 0 Ignore the factor 2.Subproblem 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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