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Simplifying (5b + 2)(9b + -10) = 0 Reorder the terms: (2 + 5b)(9b + -10) = 0 Reorder the terms: (2 + 5b)(-10 + 9b) = 0 Multiply (2 + 5b) * (-10 + 9b) (2(-10 + 9b) + 5b * (-10 + 9b)) = 0 ((-10 * 2 + 9b * 2) + 5b * (-10 + 9b)) = 0 ((-20 + 18b) + 5b * (-10 + 9b)) = 0 (-20 + 18b + (-10 * 5b + 9b * 5b)) = 0 (-20 + 18b + (-50b + 45b2)) = 0 Combine like terms: 18b + -50b = -32b (-20 + -32b + 45b2) = 0 Solving -20 + -32b + 45b2 = 0 Solving for variable 'b'. Factor a trinomial. (-2 + -5b)(10 + -9b) = 0Subproblem 1
Set the factor '(-2 + -5b)' equal to zero and attempt to solve: Simplifying -2 + -5b = 0 Solving -2 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -5b = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5b = 0 + 2 -5b = 0 + 2 Combine like terms: 0 + 2 = 2 -5b = 2 Divide each side by '-5'. b = -0.4 Simplifying b = -0.4Subproblem 2
Set the factor '(10 + -9b)' equal to zero and attempt to solve: Simplifying 10 + -9b = 0 Solving 10 + -9b = 0 Move all terms containing b to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -9b = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -9b = 0 + -10 -9b = 0 + -10 Combine like terms: 0 + -10 = -10 -9b = -10 Divide each side by '-9'. b = 1.111111111 Simplifying b = 1.111111111Solution
b = {-0.4, 1.111111111}
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