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Simplifying -12b4u + -18b3u + -15b2u = 0 Reorder the terms: -15b2u + -18b3u + -12b4u = 0 Solving -15b2u + -18b3u + -12b4u = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '-3b2u'. -3b2u(5 + 6b + 4b2) = 0 Ignore the factor -3.Subproblem 1
Set the factor 'b2u' equal to zero and attempt to solve: Simplifying b2u = 0 Solving b2u = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b2u = 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 '(5 + 6b + 4b2)' equal to zero and attempt to solve: Simplifying 5 + 6b + 4b2 = 0 Solving 5 + 6b + 4b2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 1.5b + b2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 1.5b + -1.25 + b2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 1.5b + b2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 1.5b + b2 = 0 + -1.25 1.5b + b2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 1.5b + b2 = -1.25 The b term is 1.5b. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5b + 0.5625 + b2 = -1.25 + 0.5625 Reorder the terms: 0.5625 + 1.5b + b2 = -1.25 + 0.5625 Combine like terms: -1.25 + 0.5625 = -0.6875 0.5625 + 1.5b + b2 = -0.6875 Factor a perfect square on the left side: (b + 0.75)(b + 0.75) = -0.6875 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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