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Simplifying 4b2 + -24 = -1b2 + 37b Reorder the terms: -24 + 4b2 = -1b2 + 37b Reorder the terms: -24 + 4b2 = 37b + -1b2 Solving -24 + 4b2 = 37b + -1b2 Solving for variable 'b'. Reorder the terms: -24 + -37b + 4b2 + b2 = 37b + -1b2 + -37b + b2 Combine like terms: 4b2 + b2 = 5b2 -24 + -37b + 5b2 = 37b + -1b2 + -37b + b2 Reorder the terms: -24 + -37b + 5b2 = 37b + -37b + -1b2 + b2 Combine like terms: 37b + -37b = 0 -24 + -37b + 5b2 = 0 + -1b2 + b2 -24 + -37b + 5b2 = -1b2 + b2 Combine like terms: -1b2 + b2 = 0 -24 + -37b + 5b2 = 0 Factor a trinomial. (-3 + -5b)(8 + -1b) = 0Subproblem 1
Set the factor '(-3 + -5b)' equal to zero and attempt to solve: Simplifying -3 + -5b = 0 Solving -3 + -5b = 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 + -5b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5b = 0 + 3 -5b = 0 + 3 Combine like terms: 0 + 3 = 3 -5b = 3 Divide each side by '-5'. b = -0.6 Simplifying b = -0.6Subproblem 2
Set the factor '(8 + -1b)' equal to zero and attempt to solve: Simplifying 8 + -1b = 0 Solving 8 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1b = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1b = 0 + -8 -1b = 0 + -8 Combine like terms: 0 + -8 = -8 -1b = -8 Divide each side by '-1'. b = 8 Simplifying b = 8Solution
b = {-0.6, 8}
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