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Simplifying p * p + 2pq + -120q * q = 0 Multiply p * p p2 + 2pq + -120q * q = 0 Multiply q * q p2 + 2pq + -120q2 = 0 Reorder the terms: 2pq + p2 + -120q2 = 0 Solving 2pq + p2 + -120q2 = 0 Solving for variable 'p'. Factor a trinomial. (p + -10q)(p + 12q) = 0Subproblem 1
Set the factor '(p + -10q)' equal to zero and attempt to solve: Simplifying p + -10q = 0 Solving p + -10q = 0 Move all terms containing p to the left, all other terms to the right. Add '10q' to each side of the equation. p + -10q + 10q = 0 + 10q Combine like terms: -10q + 10q = 0 p + 0 = 0 + 10q p = 0 + 10q Remove the zero: p = 10q Simplifying p = 10qSubproblem 2
Set the factor '(p + 12q)' equal to zero and attempt to solve: Simplifying p + 12q = 0 Solving p + 12q = 0 Move all terms containing p to the left, all other terms to the right. Add '-12q' to each side of the equation. p + 12q + -12q = 0 + -12q Combine like terms: 12q + -12q = 0 p + 0 = 0 + -12q p = 0 + -12q Remove the zero: p = -12q Simplifying p = -12qSolution
p = {10q, -12q}
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