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Simplifying 7b3 + -5b2 + 3b = 0 Reorder the terms: 3b + -5b2 + 7b3 = 0 Solving 3b + -5b2 + 7b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), 'b'. b(3 + -5b + 7b2) = 0Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(3 + -5b + 7b2)' equal to zero and attempt to solve: Simplifying 3 + -5b + 7b2 = 0 Solving 3 + -5b + 7b2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + -0.7142857143b + b2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.7142857143b + -0.4285714286 + b2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + -0.7142857143b + b2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + -0.7142857143b + b2 = 0 + -0.4285714286 -0.7142857143b + b2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 -0.7142857143b + b2 = -0.4285714286 The b term is -0.7142857143b. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143b + 0.1275510204 + b2 = -0.4285714286 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143b + b2 = -0.4285714286 + 0.1275510204 Combine like terms: -0.4285714286 + 0.1275510204 = -0.3010204082 0.1275510204 + -0.7142857143b + b2 = -0.3010204082 Factor a perfect square on the left side: (b + -0.3571428572)(b + -0.3571428572) = -0.3010204082 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
b = {0}
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