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Simplifying 42b2 + b = 30 Reorder the terms: b + 42b2 = 30 Solving b + 42b2 = 30 Solving for variable 'b'. Reorder the terms: -30 + b + 42b2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + b + 42b2 = 0 Factor a trinomial. (-6 + -7b)(5 + -6b) = 0Subproblem 1
Set the factor '(-6 + -7b)' equal to zero and attempt to solve: Simplifying -6 + -7b = 0 Solving -6 + -7b = 0 Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -7b = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7b = 0 + 6 -7b = 0 + 6 Combine like terms: 0 + 6 = 6 -7b = 6 Divide each side by '-7'. b = -0.8571428571 Simplifying b = -0.8571428571Subproblem 2
Set the factor '(5 + -6b)' equal to zero and attempt to solve: Simplifying 5 + -6b = 0 Solving 5 + -6b = 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 + -6b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6b = 0 + -5 -6b = 0 + -5 Combine like terms: 0 + -5 = -5 -6b = -5 Divide each side by '-6'. b = 0.8333333333 Simplifying b = 0.8333333333Solution
b = {-0.8571428571, 0.8333333333}
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