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Simplifying 4p4 + -25p2 + 16p2 = 0 Reorder the terms: -25p2 + 16p2 + 4p4 = 0 Combine like terms: -25p2 + 16p2 = -9p2 -9p2 + 4p4 = 0 Solving -9p2 + 4p4 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p2'. p2(-9 + 4p2) = 0 Factor a difference between two squares. p2((3 + 2p)(-3 + 2p)) = 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 '(3 + 2p)' equal to zero and attempt to solve: Simplifying 3 + 2p = 0 Solving 3 + 2p = 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 + 2p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2p = 0 + -3 2p = 0 + -3 Combine like terms: 0 + -3 = -3 2p = -3 Divide each side by '2'. p = -1.5 Simplifying p = -1.5Subproblem 3
Set the factor '(-3 + 2p)' equal to zero and attempt to solve: Simplifying -3 + 2p = 0 Solving -3 + 2p = 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 + 2p = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2p = 0 + 3 2p = 0 + 3 Combine like terms: 0 + 3 = 3 2p = 3 Divide each side by '2'. p = 1.5 Simplifying p = 1.5Solution
p = {0, -1.5, 1.5}
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