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Simplifying (7p + 5q)(7p + -5q) = 0 Multiply (7p + 5q) * (7p + -5q) (7p * (7p + -5q) + 5q * (7p + -5q)) = 0 ((7p * 7p + -5q * 7p) + 5q * (7p + -5q)) = 0 Reorder the terms: ((-35pq + 49p2) + 5q * (7p + -5q)) = 0 ((-35pq + 49p2) + 5q * (7p + -5q)) = 0 (-35pq + 49p2 + (7p * 5q + -5q * 5q)) = 0 (-35pq + 49p2 + (35pq + -25q2)) = 0 Reorder the terms: (-35pq + 35pq + 49p2 + -25q2) = 0 Combine like terms: -35pq + 35pq = 0 (0 + 49p2 + -25q2) = 0 (49p2 + -25q2) = 0 Solving 49p2 + -25q2 = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '25q2' to each side of the equation. 49p2 + -25q2 + 25q2 = 0 + 25q2 Combine like terms: -25q2 + 25q2 = 0 49p2 + 0 = 0 + 25q2 49p2 = 0 + 25q2 Remove the zero: 49p2 = 25q2 Divide each side by '49'. p2 = 0.5102040816q2 Simplifying p2 = 0.5102040816q2 Take the square root of each side: p = {-0.714285714q, 0.714285714q}
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