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Simplifying 32b5 + -12b4 + 48b3 = 0 Reorder the terms: 48b3 + -12b4 + 32b5 = 0 Solving 48b3 + -12b4 + 32b5 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4b3'. 4b3(12 + -3b + 8b2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'b3' equal to zero and attempt to solve: Simplifying b3 = 0 Solving b3 = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(12 + -3b + 8b2)' equal to zero and attempt to solve: Simplifying 12 + -3b + 8b2 = 0 Solving 12 + -3b + 8b2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.5 + -0.375b + b2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -0.375b + -1.5 + b2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -0.375b + b2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -0.375b + b2 = 0 + -1.5 -0.375b + b2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -0.375b + b2 = -1.5 The b term is -0.375b. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375b + 0.03515625 + b2 = -1.5 + 0.03515625 Reorder the terms: 0.03515625 + -0.375b + b2 = -1.5 + 0.03515625 Combine like terms: -1.5 + 0.03515625 = -1.46484375 0.03515625 + -0.375b + b2 = -1.46484375 Factor a perfect square on the left side: (b + -0.1875)(b + -0.1875) = -1.46484375 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. The solution to this equation could not be determined.
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