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Simplifying -2b3 + -32b2 + -450b = 0 Reorder the terms: -450b + -32b2 + -2b3 = 0 Solving -450b + -32b2 + -2b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '-2b'. -2b(225 + 16b + 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 '(225 + 16b + b2)' equal to zero and attempt to solve: Simplifying 225 + 16b + b2 = 0 Solving 225 + 16b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-225' to each side of the equation. 225 + 16b + -225 + b2 = 0 + -225 Reorder the terms: 225 + -225 + 16b + b2 = 0 + -225 Combine like terms: 225 + -225 = 0 0 + 16b + b2 = 0 + -225 16b + b2 = 0 + -225 Combine like terms: 0 + -225 = -225 16b + b2 = -225 The b term is 16b. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16b + 64 + b2 = -225 + 64 Reorder the terms: 64 + 16b + b2 = -225 + 64 Combine like terms: -225 + 64 = -161 64 + 16b + b2 = -161 Factor a perfect square on the left side: (b + 8)(b + 8) = -161 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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