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Simplifying 2p4 + -32q4 = 0 Solving 2p4 + -32q4 = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '32q4' to each side of the equation. 2p4 + -32q4 + 32q4 = 0 + 32q4 Combine like terms: -32q4 + 32q4 = 0 2p4 + 0 = 0 + 32q4 2p4 = 0 + 32q4 Remove the zero: 2p4 = 32q4 Divide each side by '2'. p4 = 16q4 Simplifying p4 = 16q4 Combine like terms: 16q4 + -16q4 = 0 p4 + -16q4 = 0 Factor a difference between two squares. (p2 + 4q2)(p2 + -4q2) = 0 Factor a difference between two squares. (p2 + 4q2)((p + 2q)(p + -2q)) = 0Subproblem 1
Set the factor '(p2 + 4q2)' equal to zero and attempt to solve: Simplifying p2 + 4q2 = 0 Solving p2 + 4q2 = 0 Move all terms containing p to the left, all other terms to the right. Add '-4q2' to each side of the equation. p2 + 4q2 + -4q2 = 0 + -4q2 Combine like terms: 4q2 + -4q2 = 0 p2 + 0 = 0 + -4q2 p2 = 0 + -4q2 Remove the zero: p2 = -4q2 Simplifying p2 = -4q2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(p + 2q)' equal to zero and attempt to solve: Simplifying p + 2q = 0 Solving p + 2q = 0 Move all terms containing p to the left, all other terms to the right. Add '-2q' to each side of the equation. p + 2q + -2q = 0 + -2q Combine like terms: 2q + -2q = 0 p + 0 = 0 + -2q p = 0 + -2q Remove the zero: p = -2q Simplifying p = -2qSubproblem 3
Set the factor '(p + -2q)' equal to zero and attempt to solve: Simplifying p + -2q = 0 Solving p + -2q = 0 Move all terms containing p to the left, all other terms to the right. Add '2q' to each side of the equation. p + -2q + 2q = 0 + 2q Combine like terms: -2q + 2q = 0 p + 0 = 0 + 2q p = 0 + 2q Remove the zero: p = 2q Simplifying p = 2qSolution
p = {-2q, 2q}
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