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Simplifying 138b + 48b2 + -81 = 0 Reorder the terms: -81 + 138b + 48b2 = 0 Solving -81 + 138b + 48b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(-27 + 46b + 16b2) = 0 Factor a trinomial. 3((-27 + -8b)(1 + -2b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-27 + -8b)' equal to zero and attempt to solve: Simplifying -27 + -8b = 0 Solving -27 + -8b = 0 Move all terms containing b to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + -8b = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -8b = 0 + 27 -8b = 0 + 27 Combine like terms: 0 + 27 = 27 -8b = 27 Divide each side by '-8'. b = -3.375 Simplifying b = -3.375Subproblem 2
Set the factor '(1 + -2b)' equal to zero and attempt to solve: Simplifying 1 + -2b = 0 Solving 1 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2b = 0 + -1 -2b = 0 + -1 Combine like terms: 0 + -1 = -1 -2b = -1 Divide each side by '-2'. b = 0.5 Simplifying b = 0.5Solution
b = {-3.375, 0.5}
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