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Simplifying 25p2 + 145p + 100 = 0 Reorder the terms: 100 + 145p + 25p2 = 0 Solving 100 + 145p + 25p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5'. 5(20 + 29p + 5p2) = 0 Factor a trinomial. 5((5 + p)(4 + 5p)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + p)' equal to zero and attempt to solve: Simplifying 5 + p = 0 Solving 5 + p = 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 + p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + p = 0 + -5 p = 0 + -5 Combine like terms: 0 + -5 = -5 p = -5 Simplifying p = -5Subproblem 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 = {-5, -0.8}
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