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Simplifying -12b4p + -6b3p + -21b2p = 0 Reorder the terms: -21b2p + -6b3p + -12b4p = 0 Solving -21b2p + -6b3p + -12b4p = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '-3b2p'. -3b2p(7 + 2b + 4b2) = 0 Ignore the factor -3.Subproblem 1
Set the factor 'b2p' equal to zero and attempt to solve: Simplifying b2p = 0 Solving b2p = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b2p = 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 '(7 + 2b + 4b2)' equal to zero and attempt to solve: Simplifying 7 + 2b + 4b2 = 0 Solving 7 + 2b + 4b2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 0.5b + b2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 0.5b + -1.75 + b2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 0.5b + b2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 0.5b + b2 = 0 + -1.75 0.5b + b2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 0.5b + b2 = -1.75 The b term is 0.5b. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5b + 0.0625 + b2 = -1.75 + 0.0625 Reorder the terms: 0.0625 + 0.5b + b2 = -1.75 + 0.0625 Combine like terms: -1.75 + 0.0625 = -1.6875 0.0625 + 0.5b + b2 = -1.6875 Factor a perfect square on the left side: (b + 0.25)(b + 0.25) = -1.6875 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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