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Simplifying 40p2 + 183p + -168 = p + 5p2 Reorder the terms: -168 + 183p + 40p2 = p + 5p2 Solving -168 + 183p + 40p2 = p + 5p2 Solving for variable 'p'. Reorder the terms: -168 + 183p + -1p + 40p2 + -5p2 = p + 5p2 + -1p + -5p2 Combine like terms: 183p + -1p = 182p -168 + 182p + 40p2 + -5p2 = p + 5p2 + -1p + -5p2 Combine like terms: 40p2 + -5p2 = 35p2 -168 + 182p + 35p2 = p + 5p2 + -1p + -5p2 Reorder the terms: -168 + 182p + 35p2 = p + -1p + 5p2 + -5p2 Combine like terms: p + -1p = 0 -168 + 182p + 35p2 = 0 + 5p2 + -5p2 -168 + 182p + 35p2 = 5p2 + -5p2 Combine like terms: 5p2 + -5p2 = 0 -168 + 182p + 35p2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-24 + 26p + 5p2) = 0 Factor a trinomial. 7((-6 + -1p)(4 + -5p)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-6 + -1p)' equal to zero and attempt to solve: Simplifying -6 + -1p = 0 Solving -6 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1p = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1p = 0 + 6 -1p = 0 + 6 Combine like terms: 0 + 6 = 6 -1p = 6 Divide each side by '-1'. p = -6 Simplifying p = -6Subproblem 2
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 = 0.8Solution
p = {-6, 0.8}
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