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Simplifying 9b2 = 24 + 30b Solving 9b2 = 24 + 30b Solving for variable 'b'. Reorder the terms: -24 + -30b + 9b2 = 24 + 30b + -24 + -30b Reorder the terms: -24 + -30b + 9b2 = 24 + -24 + 30b + -30b Combine like terms: 24 + -24 = 0 -24 + -30b + 9b2 = 0 + 30b + -30b -24 + -30b + 9b2 = 30b + -30b Combine like terms: 30b + -30b = 0 -24 + -30b + 9b2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + -10b + 3b2) = 0 Factor a trinomial. 3((-2 + -3b)(4 + -1b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -3b)' equal to zero and attempt to solve: Simplifying -2 + -3b = 0 Solving -2 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3b = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3b = 0 + 2 -3b = 0 + 2 Combine like terms: 0 + 2 = 2 -3b = 2 Divide each side by '-3'. b = -0.6666666667 Simplifying b = -0.6666666667Subproblem 2
Set the factor '(4 + -1b)' equal to zero and attempt to solve: Simplifying 4 + -1b = 0 Solving 4 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1b = 0 + -4 -1b = 0 + -4 Combine like terms: 0 + -4 = -4 -1b = -4 Divide each side by '-1'. b = 4 Simplifying b = 4Solution
b = {-0.6666666667, 4}
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