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Simplifying (9sqr + -1) * 8(-6sqr + -4) = 0 Reorder the terms: (-1 + 9qrs) * 8(-6sqr + -4) = 0 Reorder the terms: (-1 + 9qrs) * 8(-4 + -6qrs) = 0 Reorder the terms for easier multiplication: 8(-1 + 9qrs)(-4 + -6qrs) = 0 Multiply (-1 + 9qrs) * (-4 + -6qrs) 8(-1(-4 + -6qrs) + 9qrs * (-4 + -6qrs)) = 0 8((-4 * -1 + -6qrs * -1) + 9qrs * (-4 + -6qrs)) = 0 8((4 + 6qrs) + 9qrs * (-4 + -6qrs)) = 0 8(4 + 6qrs + (-4 * 9qrs + -6qrs * 9qrs)) = 0 8(4 + 6qrs + (-36qrs + -54q2r2s2)) = 0 Combine like terms: 6qrs + -36qrs = -30qrs 8(4 + -30qrs + -54q2r2s2) = 0 (4 * 8 + -30qrs * 8 + -54q2r2s2 * 8) = 0 (32 + -240qrs + -432q2r2s2) = 0 Solving 32 + -240qrs + -432q2r2s2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '16'. 16(2 + -15qrs + -27q2r2s2) = 0 Factor a trinomial. 16((1 + -9qrs)(2 + 3qrs)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(1 + -9qrs)' equal to zero and attempt to solve: Simplifying 1 + -9qrs = 0 Solving 1 + -9qrs = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -9qrs = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9qrs = 0 + -1 -9qrs = 0 + -1 Combine like terms: 0 + -1 = -1 -9qrs = -1 Divide each side by '-9rs'. q = 0.1111111111r-1s-1 Simplifying q = 0.1111111111r-1s-1Subproblem 2
Set the factor '(2 + 3qrs)' equal to zero and attempt to solve: Simplifying 2 + 3qrs = 0 Solving 2 + 3qrs = 0 Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3qrs = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3qrs = 0 + -2 3qrs = 0 + -2 Combine like terms: 0 + -2 = -2 3qrs = -2 Divide each side by '3rs'. q = -0.6666666667r-1s-1 Simplifying q = -0.6666666667r-1s-1Solution
q = {0.1111111111r-1s-1, -0.6666666667r-1s-1}
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