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Simplifying 2q4 + 9q3 + -18q2 = 0 Reorder the terms: -18q2 + 9q3 + 2q4 = 0 Solving -18q2 + 9q3 + 2q4 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), 'q2'. q2(-18 + 9q + 2q2) = 0 Factor a trinomial. q2((-6 + -1q)(3 + -2q)) = 0Subproblem 1
Set the factor 'q2' equal to zero and attempt to solve: Simplifying q2 = 0 Solving q2 = 0 Move all terms containing q to the left, all other terms to the right. Simplifying q2 = 0 Take the square root of each side: q = {0}Subproblem 2
Set the factor '(-6 + -1q)' equal to zero and attempt to solve: Simplifying -6 + -1q = 0 Solving -6 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1q = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1q = 0 + 6 -1q = 0 + 6 Combine like terms: 0 + 6 = 6 -1q = 6 Divide each side by '-1'. q = -6 Simplifying q = -6Subproblem 3
Set the factor '(3 + -2q)' equal to zero and attempt to solve: Simplifying 3 + -2q = 0 Solving 3 + -2q = 0 Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2q = 0 + -3 -2q = 0 + -3 Combine like terms: 0 + -3 = -3 -2q = -3 Divide each side by '-2'. q = 1.5 Simplifying q = 1.5Solution
q = {0, -6, 1.5}
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