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Simplifying 40p2 = 16 + -12p Solving 40p2 = 16 + -12p Solving for variable 'p'. Reorder the terms: -16 + 12p + 40p2 = 16 + -12p + -16 + 12p Reorder the terms: -16 + 12p + 40p2 = 16 + -16 + -12p + 12p Combine like terms: 16 + -16 = 0 -16 + 12p + 40p2 = 0 + -12p + 12p -16 + 12p + 40p2 = -12p + 12p Combine like terms: -12p + 12p = 0 -16 + 12p + 40p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 3p + 10p2) = 0 Factor a trinomial. 4((-4 + -5p)(1 + -2p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -5p)' equal to zero and attempt to solve: Simplifying -4 + -5p = 0 Solving -4 + -5p = 0 Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5p = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5p = 0 + 4 -5p = 0 + 4 Combine like terms: 0 + 4 = 4 -5p = 4 Divide each side by '-5'. p = -0.8 Simplifying p = -0.8Subproblem 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 = {-0.8, 0.5}
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