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Simplifying 108 + 100b2 + -240b = 0 Reorder the terms: 108 + -240b + 100b2 = 0 Solving 108 + -240b + 100b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4'. 4(27 + -60b + 25b2) = 0 Factor a trinomial. 4((3 + -5b)(9 + -5b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -5b)' equal to zero and attempt to solve: Simplifying 3 + -5b = 0 Solving 3 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5b = 0 + -3 -5b = 0 + -3 Combine like terms: 0 + -3 = -3 -5b = -3 Divide each side by '-5'. b = 0.6 Simplifying b = 0.6Subproblem 2
Set the factor '(9 + -5b)' equal to zero and attempt to solve: Simplifying 9 + -5b = 0 Solving 9 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5b = 0 + -9 -5b = 0 + -9 Combine like terms: 0 + -9 = -9 -5b = -9 Divide each side by '-5'. b = 1.8 Simplifying b = 1.8Solution
b = {0.6, 1.8}
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