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Simplifying 40p2 = 28 + -36p Solving 40p2 = 28 + -36p Solving for variable 'p'. Reorder the terms: -28 + 36p + 40p2 = 28 + -36p + -28 + 36p Reorder the terms: -28 + 36p + 40p2 = 28 + -28 + -36p + 36p Combine like terms: 28 + -28 = 0 -28 + 36p + 40p2 = 0 + -36p + 36p -28 + 36p + 40p2 = -36p + 36p Combine like terms: -36p + 36p = 0 -28 + 36p + 40p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-7 + 9p + 10p2) = 0 Factor a trinomial. 4((-7 + -5p)(1 + -2p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -5p)' equal to zero and attempt to solve: Simplifying -7 + -5p = 0 Solving -7 + -5p = 0 Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -5p = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5p = 0 + 7 -5p = 0 + 7 Combine like terms: 0 + 7 = 7 -5p = 7 Divide each side by '-5'. p = -1.4 Simplifying p = -1.4Subproblem 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 = {-1.4, 0.5}
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