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Simplifying 9q4 + -42q3 + 49q2 = 0 Reorder the terms: 49q2 + -42q3 + 9q4 = 0 Solving 49q2 + -42q3 + 9q4 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), 'q2'. q2(49 + -42q + 9q2) = 0 Factor a trinomial. q2((7 + -3q)(7 + -3q)) = 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 '(7 + -3q)' equal to zero and attempt to solve: Simplifying 7 + -3q = 0 Solving 7 + -3q = 0 Move all terms containing q to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3q = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3q = 0 + -7 -3q = 0 + -7 Combine like terms: 0 + -7 = -7 -3q = -7 Divide each side by '-3'. q = 2.333333333 Simplifying q = 2.333333333Subproblem 3
Set the factor '(7 + -3q)' equal to zero and attempt to solve: Simplifying 7 + -3q = 0 Solving 7 + -3q = 0 Move all terms containing q to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3q = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3q = 0 + -7 -3q = 0 + -7 Combine like terms: 0 + -7 = -7 -3q = -7 Divide each side by '-3'. q = 2.333333333 Simplifying q = 2.333333333Solution
q = {0, 2.333333333, 2.333333333}
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