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Simplifying 40b2 = 44b + 24 Reorder the terms: 40b2 = 24 + 44b Solving 40b2 = 24 + 44b Solving for variable 'b'. Reorder the terms: -24 + -44b + 40b2 = 24 + 44b + -24 + -44b Reorder the terms: -24 + -44b + 40b2 = 24 + -24 + 44b + -44b Combine like terms: 24 + -24 = 0 -24 + -44b + 40b2 = 0 + 44b + -44b -24 + -44b + 40b2 = 44b + -44b Combine like terms: 44b + -44b = 0 -24 + -44b + 40b2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + -11b + 10b2) = 0 Factor a trinomial. 4((-2 + -5b)(3 + -2b)) = 0 Ignore the factor 4.Subproblem 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 '(3 + -2b)' equal to zero and attempt to solve: Simplifying 3 + -2b = 0 Solving 3 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2b = 0 + -3 -2b = 0 + -3 Combine like terms: 0 + -3 = -3 -2b = -3 Divide each side by '-2'. b = 1.5 Simplifying b = 1.5Solution
b = {-0.4, 1.5}
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