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Simplifying 400b3 + -820b2 + 400b = 0 Reorder the terms: 400b + -820b2 + 400b3 = 0 Solving 400b + -820b2 + 400b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '20b'. 20b(20 + -41b + 20b2) = 0 Factor a trinomial. 20b((4 + -5b)(5 + -4b)) = 0 Ignore the factor 20.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(4 + -5b)' equal to zero and attempt to solve: Simplifying 4 + -5b = 0 Solving 4 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5b = 0 + -4 -5b = 0 + -4 Combine like terms: 0 + -4 = -4 -5b = -4 Divide each side by '-5'. b = 0.8 Simplifying b = 0.8Subproblem 3
Set the factor '(5 + -4b)' equal to zero and attempt to solve: Simplifying 5 + -4b = 0 Solving 5 + -4b = 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 + -4b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4b = 0 + -5 -4b = 0 + -5 Combine like terms: 0 + -5 = -5 -4b = -5 Divide each side by '-4'. b = 1.25 Simplifying b = 1.25Solution
b = {0, 0.8, 1.25}
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