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Simplifying 100 + -100q + 24q2 = 0 Solving 100 + -100q + 24q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '4'. 4(25 + -25q + 6q2) = 0 Factor a trinomial. 4((5 + -3q)(5 + -2q)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -3q)' equal to zero and attempt to solve: Simplifying 5 + -3q = 0 Solving 5 + -3q = 0 Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3q = 0 + -5 -3q = 0 + -5 Combine like terms: 0 + -5 = -5 -3q = -5 Divide each side by '-3'. q = 1.666666667 Simplifying q = 1.666666667Subproblem 2
Set the factor '(5 + -2q)' equal to zero and attempt to solve: Simplifying 5 + -2q = 0 Solving 5 + -2q = 0 Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2q = 0 + -5 -2q = 0 + -5 Combine like terms: 0 + -5 = -5 -2q = -5 Divide each side by '-2'. q = 2.5 Simplifying q = 2.5Solution
q = {1.666666667, 2.5}
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