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Simplifying 8p2 + 32 = 40p Reorder the terms: 32 + 8p2 = 40p Solving 32 + 8p2 = 40p Solving for variable 'p'. Reorder the terms: 32 + -40p + 8p2 = 40p + -40p Combine like terms: 40p + -40p = 0 32 + -40p + 8p2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(4 + -5p + p2) = 0 Factor a trinomial. 8((1 + -1p)(4 + -1p)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + -1p)' equal to zero and attempt to solve: Simplifying 1 + -1p = 0 Solving 1 + -1p = 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 + -1p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1p = 0 + -1 -1p = 0 + -1 Combine like terms: 0 + -1 = -1 -1p = -1 Divide each side by '-1'. p = 1 Simplifying p = 1Subproblem 2
Set the factor '(4 + -1p)' equal to zero and attempt to solve: Simplifying 4 + -1p = 0 Solving 4 + -1p = 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 + -1p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1p = 0 + -4 -1p = 0 + -4 Combine like terms: 0 + -4 = -4 -1p = -4 Divide each side by '-1'. p = 4 Simplifying p = 4Solution
p = {1, 4}
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