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Simplifying 0 = 10b2 + -27b + 18 Reorder the terms: 0 = 18 + -27b + 10b2 Solving 0 = 18 + -27b + 10b2 Solving for variable 'b'. Combine like terms: 0 + -18 = -18 -18 + 27b + -10b2 = 18 + -27b + 10b2 + -18 + 27b + -10b2 Reorder the terms: -18 + 27b + -10b2 = 18 + -18 + -27b + 27b + 10b2 + -10b2 Combine like terms: 18 + -18 = 0 -18 + 27b + -10b2 = 0 + -27b + 27b + 10b2 + -10b2 -18 + 27b + -10b2 = -27b + 27b + 10b2 + -10b2 Combine like terms: -27b + 27b = 0 -18 + 27b + -10b2 = 0 + 10b2 + -10b2 -18 + 27b + -10b2 = 10b2 + -10b2 Combine like terms: 10b2 + -10b2 = 0 -18 + 27b + -10b2 = 0 Factor a trinomial. (-3 + 2b)(6 + -5b) = 0Subproblem 1
Set the factor '(-3 + 2b)' equal to zero and attempt to solve: Simplifying -3 + 2b = 0 Solving -3 + 2b = 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 + 2b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2b = 0 + 3 2b = 0 + 3 Combine like terms: 0 + 3 = 3 2b = 3 Divide each side by '2'. b = 1.5 Simplifying b = 1.5Subproblem 2
Set the factor '(6 + -5b)' equal to zero and attempt to solve: Simplifying 6 + -5b = 0 Solving 6 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5b = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5b = 0 + -6 -5b = 0 + -6 Combine like terms: 0 + -6 = -6 -5b = -6 Divide each side by '-5'. b = 1.2 Simplifying b = 1.2Solution
b = {1.5, 1.2}
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