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Simplifying 5b2 + -19b + -27 = -3 Reorder the terms: -27 + -19b + 5b2 = -3 Solving -27 + -19b + 5b2 = -3 Solving for variable 'b'. Reorder the terms: -27 + 3 + -19b + 5b2 = -3 + 3 Combine like terms: -27 + 3 = -24 -24 + -19b + 5b2 = -3 + 3 Combine like terms: -3 + 3 = 0 -24 + -19b + 5b2 = 0 Factor a trinomial. (-1 + -1b)(24 + -5b) = 0Subproblem 1
Set the factor '(-1 + -1b)' equal to zero and attempt to solve: Simplifying -1 + -1b = 0 Solving -1 + -1b = 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 + -1b = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1b = 0 + 1 -1b = 0 + 1 Combine like terms: 0 + 1 = 1 -1b = 1 Divide each side by '-1'. b = -1 Simplifying b = -1Subproblem 2
Set the factor '(24 + -5b)' equal to zero and attempt to solve: Simplifying 24 + -5b = 0 Solving 24 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + -5b = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -5b = 0 + -24 -5b = 0 + -24 Combine like terms: 0 + -24 = -24 -5b = -24 Divide each side by '-5'. b = 4.8 Simplifying b = 4.8Solution
b = {-1, 4.8}
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