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Simplifying (0.1p + -0.1q)(0.1p + 0.1q)(0.001p2 + 0.001q2) = 0 Multiply (0.1p + -0.1q) * (0.1p + 0.1q) (0.1p * (0.1p + 0.1q) + -0.1q * (0.1p + 0.1q))(0.001p2 + 0.001q2) = 0 ((0.1p * 0.1p + 0.1q * 0.1p) + -0.1q * (0.1p + 0.1q))(0.001p2 + 0.001q2) = 0 Reorder the terms: ((0.01pq + 0.01p2) + -0.1q * (0.1p + 0.1q))(0.001p2 + 0.001q2) = 0 ((0.01pq + 0.01p2) + -0.1q * (0.1p + 0.1q))(0.001p2 + 0.001q2) = 0 (0.01pq + 0.01p2 + (0.1p * -0.1q + 0.1q * -0.1q))(0.001p2 + 0.001q2) = 0 (0.01pq + 0.01p2 + (-0.01pq + -0.01q2))(0.001p2 + 0.001q2) = 0 Reorder the terms: (0.01pq + -0.01pq + 0.01p2 + -0.01q2)(0.001p2 + 0.001q2) = 0 Combine like terms: 0.01pq + -0.01pq = 0.00 (0.00 + 0.01p2 + -0.01q2)(0.001p2 + 0.001q2) = 0 (0.01p2 + -0.01q2)(0.001p2 + 0.001q2) = 0 Multiply (0.01p2 + -0.01q2) * (0.001p2 + 0.001q2) (0.01p2 * (0.001p2 + 0.001q2) + -0.01q2 * (0.001p2 + 0.001q2)) = 0 ((0.001p2 * 0.01p2 + 0.001q2 * 0.01p2) + -0.01q2 * (0.001p2 + 0.001q2)) = 0 Reorder the terms: ((0.00001p2q2 + 0.00001p4) + -0.01q2 * (0.001p2 + 0.001q2)) = 0 ((0.00001p2q2 + 0.00001p4) + -0.01q2 * (0.001p2 + 0.001q2)) = 0 (0.00001p2q2 + 0.00001p4 + (0.001p2 * -0.01q2 + 0.001q2 * -0.01q2)) = 0 (0.00001p2q2 + 0.00001p4 + (-0.00001p2q2 + -0.00001q4)) = 0 Reorder the terms: (0.00001p2q2 + -0.00001p2q2 + 0.00001p4 + -0.00001q4) = 0 Combine like terms: 0.00001p2q2 + -0.00001p2q2 = 0.00000 (0.00000 + 0.00001p4 + -0.00001q4) = 0 (0.00001p4 + -0.00001q4) = 0 Solving 0.00001p4 + -0.00001q4 = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.00001q4' to each side of the equation. 0.00001p4 + -0.00001q4 + 0.00001q4 = 0 + 0.00001q4 Combine like terms: -0.00001q4 + 0.00001q4 = 0.00000 0.00001p4 + 0.00000 = 0 + 0.00001q4 0.00001p4 = 0 + 0.00001q4 Remove the zero: 0.00001p4 = 0.00001q4 Divide each side by '0.00001'. p4 = q4 Simplifying p4 = q4 Combine like terms: q4 + -1q4 = 0 p4 + -1q4 = 0 Factor a difference between two squares. (p2 + q2)(p2 + -1q2) = 0 Factor a difference between two squares. (p2 + q2)((p + q)(p + -1q)) = 0Subproblem 1
Set the factor '(p2 + q2)' equal to zero and attempt to solve: Simplifying p2 + q2 = 0 Solving p2 + q2 = 0 Move all terms containing p to the left, all other terms to the right. Add '-1q2' to each side of the equation. p2 + q2 + -1q2 = 0 + -1q2 Combine like terms: q2 + -1q2 = 0 p2 + 0 = 0 + -1q2 p2 = 0 + -1q2 Remove the zero: p2 = -1q2 Simplifying p2 = -1q2 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 + q)' equal to zero and attempt to solve: Simplifying p + q = 0 Solving p + q = 0 Move all terms containing p to the left, all other terms to the right. Add '-1q' to each side of the equation. p + q + -1q = 0 + -1q Combine like terms: q + -1q = 0 p + 0 = 0 + -1q p = 0 + -1q Remove the zero: p = -1q Simplifying p = -1qSubproblem 3
Set the factor '(p + -1q)' equal to zero and attempt to solve: Simplifying p + -1q = 0 Solving p + -1q = 0 Move all terms containing p to the left, all other terms to the right. Add 'q' to each side of the equation. p + -1q + q = 0 + q Combine like terms: -1q + q = 0 p + 0 = 0 + q p = 0 + q Remove the zero: p = q Simplifying p = qSolution
p = {-1q, q}
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