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Simplifying (2b + -1)(5b + 7) = 0 Reorder the terms: (-1 + 2b)(5b + 7) = 0 Reorder the terms: (-1 + 2b)(7 + 5b) = 0 Multiply (-1 + 2b) * (7 + 5b) (-1(7 + 5b) + 2b * (7 + 5b)) = 0 ((7 * -1 + 5b * -1) + 2b * (7 + 5b)) = 0 ((-7 + -5b) + 2b * (7 + 5b)) = 0 (-7 + -5b + (7 * 2b + 5b * 2b)) = 0 (-7 + -5b + (14b + 10b2)) = 0 Combine like terms: -5b + 14b = 9b (-7 + 9b + 10b2) = 0 Solving -7 + 9b + 10b2 = 0 Solving for variable 'b'. Factor a trinomial. (-7 + -5b)(1 + -2b) = 0Subproblem 1
Set the factor '(-7 + -5b)' equal to zero and attempt to solve: Simplifying -7 + -5b = 0 Solving -7 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -5b = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5b = 0 + 7 -5b = 0 + 7 Combine like terms: 0 + 7 = 7 -5b = 7 Divide each side by '-5'. b = -1.4 Simplifying b = -1.4Subproblem 2
Set the factor '(1 + -2b)' equal to zero and attempt to solve: Simplifying 1 + -2b = 0 Solving 1 + -2b = 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 + -2b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2b = 0 + -1 -2b = 0 + -1 Combine like terms: 0 + -1 = -1 -2b = -1 Divide each side by '-2'. b = 0.5 Simplifying b = 0.5Solution
b = {-1.4, 0.5}
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