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Simplifying 5b2 = 11b + 12 Reorder the terms: 5b2 = 12 + 11b Solving 5b2 = 12 + 11b Solving for variable 'b'. Reorder the terms: -12 + -11b + 5b2 = 12 + 11b + -12 + -11b Reorder the terms: -12 + -11b + 5b2 = 12 + -12 + 11b + -11b Combine like terms: 12 + -12 = 0 -12 + -11b + 5b2 = 0 + 11b + -11b -12 + -11b + 5b2 = 11b + -11b Combine like terms: 11b + -11b = 0 -12 + -11b + 5b2 = 0 Factor a trinomial. (-4 + -5b)(3 + -1b) = 0Subproblem 1
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 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve: Simplifying 3 + -1b = 0 Solving 3 + -1b = 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 + -1b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1b = 0 + -3 -1b = 0 + -3 Combine like terms: 0 + -3 = -3 -1b = -3 Divide each side by '-1'. b = 3 Simplifying b = 3Solution
b = {-0.8, 3}
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