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Simplifying 35p2 + 56pq + -147q2 = 0 Reorder the terms: 56pq + 35p2 + -147q2 = 0 Solving 56pq + 35p2 + -147q2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '7'. 7(8pq + 5p2 + -21q2) = 0 Factor a trinomial. 7((5p + -7q)(p + 3q)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(5p + -7q)' equal to zero and attempt to solve: Simplifying 5p + -7q = 0 Solving 5p + -7q = 0 Move all terms containing p to the left, all other terms to the right. Add '7q' to each side of the equation. 5p + -7q + 7q = 0 + 7q Combine like terms: -7q + 7q = 0 5p + 0 = 0 + 7q 5p = 0 + 7q Remove the zero: 5p = 7q Divide each side by '5'. p = 1.4q Simplifying p = 1.4qSubproblem 2
Set the factor '(p + 3q)' equal to zero and attempt to solve: Simplifying p + 3q = 0 Solving p + 3q = 0 Move all terms containing p to the left, all other terms to the right. Add '-3q' to each side of the equation. p + 3q + -3q = 0 + -3q Combine like terms: 3q + -3q = 0 p + 0 = 0 + -3q p = 0 + -3q Remove the zero: p = -3q Simplifying p = -3qSolution
p = {1.4q, -3q}
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