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Simplifying 5p2 + 40p + 100 = 25 Reorder the terms: 100 + 40p + 5p2 = 25 Solving 100 + 40p + 5p2 = 25 Solving for variable 'p'. Reorder the terms: 100 + -25 + 40p + 5p2 = 25 + -25 Combine like terms: 100 + -25 = 75 75 + 40p + 5p2 = 25 + -25 Combine like terms: 25 + -25 = 0 75 + 40p + 5p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(15 + 8p + p2) = 0 Factor a trinomial. 5((5 + p)(3 + p)) = 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 '(3 + p)' equal to zero and attempt to solve: Simplifying 3 + p = 0 Solving 3 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + p = 0 + -3 p = 0 + -3 Combine like terms: 0 + -3 = -3 p = -3 Simplifying p = -3Solution
p = {-5, -3}
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