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Simplifying 30p2 = 14 + -32p Solving 30p2 = 14 + -32p Solving for variable 'p'. Reorder the terms: -14 + 32p + 30p2 = 14 + -32p + -14 + 32p Reorder the terms: -14 + 32p + 30p2 = 14 + -14 + -32p + 32p Combine like terms: 14 + -14 = 0 -14 + 32p + 30p2 = 0 + -32p + 32p -14 + 32p + 30p2 = -32p + 32p Combine like terms: -32p + 32p = 0 -14 + 32p + 30p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 16p + 15p2) = 0 Factor a trinomial. 2((-7 + -5p)(1 + -3p)) = 0 Ignore the factor 2.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 + -3p)' equal to zero and attempt to solve: Simplifying 1 + -3p = 0 Solving 1 + -3p = 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 + -3p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3p = 0 + -1 -3p = 0 + -1 Combine like terms: 0 + -1 = -1 -3p = -1 Divide each side by '-3'. p = 0.3333333333 Simplifying p = 0.3333333333Solution
p = {-1.4, 0.3333333333}
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