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Simplifying b3 + 20b2 + 200b = 0 Reorder the terms: 200b + 20b2 + b3 = 0 Solving 200b + 20b2 + b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), 'b'. b(200 + 20b + b2) = 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 '(200 + 20b + b2)' equal to zero and attempt to solve: Simplifying 200 + 20b + b2 = 0 Solving 200 + 20b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + 20b + -200 + b2 = 0 + -200 Reorder the terms: 200 + -200 + 20b + b2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + 20b + b2 = 0 + -200 20b + b2 = 0 + -200 Combine like terms: 0 + -200 = -200 20b + b2 = -200 The b term is 20b. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20b + 100 + b2 = -200 + 100 Reorder the terms: 100 + 20b + b2 = -200 + 100 Combine like terms: -200 + 100 = -100 100 + 20b + b2 = -100 Factor a perfect square on the left side: (b + 10)(b + 10) = -100 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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