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Simplifying 18b2 + -10b + 27b + -15 = 0 Reorder the terms: -15 + -10b + 27b + 18b2 = 0 Combine like terms: -10b + 27b = 17b -15 + 17b + 18b2 = 0 Solving -15 + 17b + 18b2 = 0 Solving for variable 'b'. Factor a trinomial. (-3 + -2b)(5 + -9b) = 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 '(5 + -9b)' equal to zero and attempt to solve: Simplifying 5 + -9b = 0 Solving 5 + -9b = 0 Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -9b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9b = 0 + -5 -9b = 0 + -5 Combine like terms: 0 + -5 = -5 -9b = -5 Divide each side by '-9'. b = 0.5555555556 Simplifying b = 0.5555555556Solution
b = {-1.5, 0.5555555556}
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