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Simplifying (5b + -1)(2b + -9) = 0 Reorder the terms: (-1 + 5b)(2b + -9) = 0 Reorder the terms: (-1 + 5b)(-9 + 2b) = 0 Multiply (-1 + 5b) * (-9 + 2b) (-1(-9 + 2b) + 5b * (-9 + 2b)) = 0 ((-9 * -1 + 2b * -1) + 5b * (-9 + 2b)) = 0 ((9 + -2b) + 5b * (-9 + 2b)) = 0 (9 + -2b + (-9 * 5b + 2b * 5b)) = 0 (9 + -2b + (-45b + 10b2)) = 0 Combine like terms: -2b + -45b = -47b (9 + -47b + 10b2) = 0 Solving 9 + -47b + 10b2 = 0 Solving for variable 'b'. Factor a trinomial. (1 + -5b)(9 + -2b) = 0Subproblem 1
Set the factor '(1 + -5b)' equal to zero and attempt to solve: Simplifying 1 + -5b = 0 Solving 1 + -5b = 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 + -5b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5b = 0 + -1 -5b = 0 + -1 Combine like terms: 0 + -1 = -1 -5b = -1 Divide each side by '-5'. b = 0.2 Simplifying b = 0.2Subproblem 2
Set the factor '(9 + -2b)' equal to zero and attempt to solve: Simplifying 9 + -2b = 0 Solving 9 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2b = 0 + -9 -2b = 0 + -9 Combine like terms: 0 + -9 = -9 -2b = -9 Divide each side by '-2'. b = 4.5 Simplifying b = 4.5Solution
b = {0.2, 4.5}
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