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Simplifying 36b2 + -12b + 1 + 36b + -6 + -40 = 0 Reorder the terms: 1 + -6 + -40 + -12b + 36b + 36b2 = 0 Combine like terms: 1 + -6 = -5 -5 + -40 + -12b + 36b + 36b2 = 0 Combine like terms: -5 + -40 = -45 -45 + -12b + 36b + 36b2 = 0 Combine like terms: -12b + 36b = 24b -45 + 24b + 36b2 = 0 Solving -45 + 24b + 36b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 8b + 12b2) = 0 Factor a trinomial. 3((-3 + -2b)(5 + -6b)) = 0 Ignore the factor 3.Subproblem 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 + -6b)' equal to zero and attempt to solve: Simplifying 5 + -6b = 0 Solving 5 + -6b = 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 + -6b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6b = 0 + -5 -6b = 0 + -5 Combine like terms: 0 + -5 = -5 -6b = -5 Divide each side by '-6'. b = 0.8333333333 Simplifying b = 0.8333333333Solution
b = {-1.5, 0.8333333333}
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