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Simplifying 6b2 + -7bc + 2c2 = 0 Reorder the terms: -7bc + 6b2 + 2c2 = 0 Solving -7bc + 6b2 + 2c2 = 0 Solving for variable 'b'. Factor a trinomial. (3b + -2c)(2b + -1c) = 0Subproblem 1
Set the factor '(3b + -2c)' equal to zero and attempt to solve: Simplifying 3b + -2c = 0 Solving 3b + -2c = 0 Move all terms containing b to the left, all other terms to the right. Add '2c' to each side of the equation. 3b + -2c + 2c = 0 + 2c Combine like terms: -2c + 2c = 0 3b + 0 = 0 + 2c 3b = 0 + 2c Remove the zero: 3b = 2c Divide each side by '3'. b = 0.6666666667c Simplifying b = 0.6666666667cSubproblem 2
Set the factor '(2b + -1c)' equal to zero and attempt to solve: Simplifying 2b + -1c = 0 Solving 2b + -1c = 0 Move all terms containing b to the left, all other terms to the right. Add 'c' to each side of the equation. 2b + -1c + c = 0 + c Combine like terms: -1c + c = 0 2b + 0 = 0 + c 2b = 0 + c Remove the zero: 2b = c Divide each side by '2'. b = 0.5c Simplifying b = 0.5cSolution
b = {0.6666666667c, 0.5c}
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