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Simplifying 32q4 + 48q3 + 18q2 = 0 Reorder the terms: 18q2 + 48q3 + 32q4 = 0 Solving 18q2 + 48q3 + 32q4 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2q2'. 2q2(9 + 24q + 16q2) = 0 Factor a trinomial. 2q2((3 + 4q)(3 + 4q)) = 0 Ignore the factor 2.Subproblem 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 '(3 + 4q)' equal to zero and attempt to solve: Simplifying 3 + 4q = 0 Solving 3 + 4q = 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 + 4q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4q = 0 + -3 4q = 0 + -3 Combine like terms: 0 + -3 = -3 4q = -3 Divide each side by '4'. q = -0.75 Simplifying q = -0.75Subproblem 3
Set the factor '(3 + 4q)' equal to zero and attempt to solve: Simplifying 3 + 4q = 0 Solving 3 + 4q = 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 + 4q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4q = 0 + -3 4q = 0 + -3 Combine like terms: 0 + -3 = -3 4q = -3 Divide each side by '4'. q = -0.75 Simplifying q = -0.75Solution
q = {0, -0.75, -0.75}
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