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Simplifying 2p3q2 + p2q + pq = 0 Reorder the terms: pq + p2q + 2p3q2 = 0 Solving pq + p2q + 2p3q2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'pq'. pq(1 + p + 2p2q) = 0Subproblem 1
Set the factor 'pq' equal to zero and attempt to solve: Simplifying pq = 0 Solving pq = 0 Move all terms containing p to the left, all other terms to the right. Simplifying pq = 0 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 '(1 + p + 2p2q)' equal to zero and attempt to solve: Simplifying 1 + p + 2p2q = 0 Solving 1 + p + 2p2q = 0 Begin completing the square. Divide all terms by 2q the coefficient of the squared term: Divide each side by '2q'. 0.5q-1 + 0.5pq-1 + p2 = 0q-1 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5q-1 + 0.5pq-1 + -0.5 + p2 = -0.5 + 0q-1 Reorder the terms: -0.5 + 0.5pq-1 + p2 + 0.5q-1 = -0.5 + 0q-1 Combine like terms: -0.5 + 0 = -0.5 -0.5 + 0.5pq-1 + p2 + 0.5q-1 = -0.5 The p term is pq-1. Take half its coefficient (0.5q-1). Square it (0.25q-2) and add it to both sides. Add '0.25q-2' to each side of the equation. -0.5 + 0.5pq-1 + p2 + 0.25q-2 + 0.5q-1 = -0.5 + 0.25q-2 Factor a perfect square on the left side: (p + 0.5q-1)(p + 0.5q-1) = -0.5 + 0.25q-2 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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