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Simplifying 27b2 + 94b = -56 + -3b2 Reorder the terms: 94b + 27b2 = -56 + -3b2 Solving 94b + 27b2 = -56 + -3b2 Solving for variable 'b'. Reorder the terms: 56 + 94b + 27b2 + 3b2 = -56 + -3b2 + 56 + 3b2 Combine like terms: 27b2 + 3b2 = 30b2 56 + 94b + 30b2 = -56 + -3b2 + 56 + 3b2 Reorder the terms: 56 + 94b + 30b2 = -56 + 56 + -3b2 + 3b2 Combine like terms: -56 + 56 = 0 56 + 94b + 30b2 = 0 + -3b2 + 3b2 56 + 94b + 30b2 = -3b2 + 3b2 Combine like terms: -3b2 + 3b2 = 0 56 + 94b + 30b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(28 + 47b + 15b2) = 0 Factor a trinomial. 2((7 + 3b)(4 + 5b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 3b)' equal to zero and attempt to solve: Simplifying 7 + 3b = 0 Solving 7 + 3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3b = 0 + -7 3b = 0 + -7 Combine like terms: 0 + -7 = -7 3b = -7 Divide each side by '3'. b = -2.333333333 Simplifying b = -2.333333333Subproblem 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 = -0.8Solution
b = {-2.333333333, -0.8}
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