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Simplifying 54b2 + 93bd + 40d2 = 0 Reorder the terms: 93bd + 54b2 + 40d2 = 0 Solving 93bd + 54b2 + 40d2 = 0 Solving for variable 'b'. Factor a trinomial. (6b + 5d)(9b + 8d) = 0Subproblem 1
Set the factor '(6b + 5d)' equal to zero and attempt to solve: Simplifying 6b + 5d = 0 Solving 6b + 5d = 0 Move all terms containing b to the left, all other terms to the right. Add '-5d' to each side of the equation. 6b + 5d + -5d = 0 + -5d Combine like terms: 5d + -5d = 0 6b + 0 = 0 + -5d 6b = 0 + -5d Remove the zero: 6b = -5d Divide each side by '6'. b = -0.8333333333d Simplifying b = -0.8333333333dSubproblem 2
Set the factor '(9b + 8d)' equal to zero and attempt to solve: Simplifying 9b + 8d = 0 Solving 9b + 8d = 0 Move all terms containing b to the left, all other terms to the right. Add '-8d' to each side of the equation. 9b + 8d + -8d = 0 + -8d Combine like terms: 8d + -8d = 0 9b + 0 = 0 + -8d 9b = 0 + -8d Remove the zero: 9b = -8d Divide each side by '9'. b = -0.8888888889d Simplifying b = -0.8888888889dSolution
b = {-0.8333333333d, -0.8888888889d}
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