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Simplifying 8(p + 5)(p + 5) + 10(p + 5) = 0 Reorder the terms: 8(5 + p)(p + 5) + 10(p + 5) = 0 Reorder the terms: 8(5 + p)(5 + p) + 10(p + 5) = 0 Multiply (5 + p) * (5 + p) 8(5(5 + p) + p(5 + p)) + 10(p + 5) = 0 8((5 * 5 + p * 5) + p(5 + p)) + 10(p + 5) = 0 8((25 + 5p) + p(5 + p)) + 10(p + 5) = 0 8(25 + 5p + (5 * p + p * p)) + 10(p + 5) = 0 8(25 + 5p + (5p + p2)) + 10(p + 5) = 0 Combine like terms: 5p + 5p = 10p 8(25 + 10p + p2) + 10(p + 5) = 0 (25 * 8 + 10p * 8 + p2 * 8) + 10(p + 5) = 0 (200 + 80p + 8p2) + 10(p + 5) = 0 Reorder the terms: 200 + 80p + 8p2 + 10(5 + p) = 0 200 + 80p + 8p2 + (5 * 10 + p * 10) = 0 200 + 80p + 8p2 + (50 + 10p) = 0 Reorder the terms: 200 + 50 + 80p + 10p + 8p2 = 0 Combine like terms: 200 + 50 = 250 250 + 80p + 10p + 8p2 = 0 Combine like terms: 80p + 10p = 90p 250 + 90p + 8p2 = 0 Solving 250 + 90p + 8p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(125 + 45p + 4p2) = 0 Factor a trinomial. 2((25 + 4p)(5 + p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 4p)' equal to zero and attempt to solve: Simplifying 25 + 4p = 0 Solving 25 + 4p = 0 Move all terms containing p to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 4p = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 4p = 0 + -25 4p = 0 + -25 Combine like terms: 0 + -25 = -25 4p = -25 Divide each side by '4'. p = -6.25 Simplifying p = -6.25Subproblem 2
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 = -5Solution
p = {-6.25, -5}
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