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Simplifying 70c2 + -165cb + 90b2 = 0 Reorder the terms: -165bc + 90b2 + 70c2 = 0 Solving -165bc + 90b2 + 70c2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '5'. 5(-33bc + 18b2 + 14c2) = 0 Factor a trinomial. 5((6b + -7c)(3b + -2c)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6b + -7c)' equal to zero and attempt to solve: Simplifying 6b + -7c = 0 Solving 6b + -7c = 0 Move all terms containing b to the left, all other terms to the right. Add '7c' to each side of the equation. 6b + -7c + 7c = 0 + 7c Combine like terms: -7c + 7c = 0 6b + 0 = 0 + 7c 6b = 0 + 7c Remove the zero: 6b = 7c Divide each side by '6'. b = 1.166666667c Simplifying b = 1.166666667cSubproblem 2
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 = 0.6666666667cSolution
b = {1.166666667c, 0.6666666667c}
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