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Simplifying 2b3 + 16b2 + 40b = 0 Reorder the terms: 40b + 16b2 + 2b3 = 0 Solving 40b + 16b2 + 2b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2b'. 2b(20 + 8b + b2) = 0 Ignore the factor 2.Subproblem 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 '(20 + 8b + b2)' equal to zero and attempt to solve: Simplifying 20 + 8b + b2 = 0 Solving 20 + 8b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 8b + -20 + b2 = 0 + -20 Reorder the terms: 20 + -20 + 8b + b2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 8b + b2 = 0 + -20 8b + b2 = 0 + -20 Combine like terms: 0 + -20 = -20 8b + b2 = -20 The b term is 8b. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8b + 16 + b2 = -20 + 16 Reorder the terms: 16 + 8b + b2 = -20 + 16 Combine like terms: -20 + 16 = -4 16 + 8b + b2 = -4 Factor a perfect square on the left side: (b + 4)(b + 4) = -4 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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