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Simplifying 6b2 = 5 + 7b Solving 6b2 = 5 + 7b Solving for variable 'b'. Reorder the terms: -5 + -7b + 6b2 = 5 + 7b + -5 + -7b Reorder the terms: -5 + -7b + 6b2 = 5 + -5 + 7b + -7b Combine like terms: 5 + -5 = 0 -5 + -7b + 6b2 = 0 + 7b + -7b -5 + -7b + 6b2 = 7b + -7b Combine like terms: 7b + -7b = 0 -5 + -7b + 6b2 = 0 Factor a trinomial. (-1 + -2b)(5 + -3b) = 0Subproblem 1
Set the factor '(-1 + -2b)' equal to zero and attempt to solve: Simplifying -1 + -2b = 0 Solving -1 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2b = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2b = 0 + 1 -2b = 0 + 1 Combine like terms: 0 + 1 = 1 -2b = 1 Divide each side by '-2'. b = -0.5 Simplifying b = -0.5Subproblem 2
Set the factor '(5 + -3b)' equal to zero and attempt to solve: Simplifying 5 + -3b = 0 Solving 5 + -3b = 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 + -3b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3b = 0 + -5 -3b = 0 + -5 Combine like terms: 0 + -5 = -5 -3b = -5 Divide each side by '-3'. b = 1.666666667 Simplifying b = 1.666666667Solution
b = {-0.5, 1.666666667}
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