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Simplifying (2b + -9)(2b + 5) = 0 Reorder the terms: (-9 + 2b)(2b + 5) = 0 Reorder the terms: (-9 + 2b)(5 + 2b) = 0 Multiply (-9 + 2b) * (5 + 2b) (-9(5 + 2b) + 2b * (5 + 2b)) = 0 ((5 * -9 + 2b * -9) + 2b * (5 + 2b)) = 0 ((-45 + -18b) + 2b * (5 + 2b)) = 0 (-45 + -18b + (5 * 2b + 2b * 2b)) = 0 (-45 + -18b + (10b + 4b2)) = 0 Combine like terms: -18b + 10b = -8b (-45 + -8b + 4b2) = 0 Solving -45 + -8b + 4b2 = 0 Solving for variable 'b'. Factor a trinomial. (-5 + -2b)(9 + -2b) = 0Subproblem 1
Set the factor '(-5 + -2b)' equal to zero and attempt to solve: Simplifying -5 + -2b = 0 Solving -5 + -2b = 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 + -2b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2b = 0 + 5 -2b = 0 + 5 Combine like terms: 0 + 5 = 5 -2b = 5 Divide each side by '-2'. b = -2.5 Simplifying b = -2.5Subproblem 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 = {-2.5, 4.5}
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