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Simplifying 81p4 + -36p3 + 4p2 = 0 Reorder the terms: 4p2 + -36p3 + 81p4 = 0 Solving 4p2 + -36p3 + 81p4 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p2'. p2(4 + -36p + 81p2) = 0 Factor a trinomial. p2((2 + -9p)(2 + -9p)) = 0Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve: Simplifying p2 = 0 Solving p2 = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p2 = 0 Take the square root of each side: p = {0}Subproblem 2
Set the factor '(2 + -9p)' equal to zero and attempt to solve: Simplifying 2 + -9p = 0 Solving 2 + -9p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -9p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9p = 0 + -2 -9p = 0 + -2 Combine like terms: 0 + -2 = -2 -9p = -2 Divide each side by '-9'. p = 0.2222222222 Simplifying p = 0.2222222222Subproblem 3
Set the factor '(2 + -9p)' equal to zero and attempt to solve: Simplifying 2 + -9p = 0 Solving 2 + -9p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -9p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9p = 0 + -2 -9p = 0 + -2 Combine like terms: 0 + -2 = -2 -9p = -2 Divide each side by '-9'. p = 0.2222222222 Simplifying p = 0.2222222222Solution
p = {0, 0.2222222222, 0.2222222222}
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