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Simplifying 8b4(3b + 6b2 + 5) = 0 Reorder the terms: 8b4(5 + 3b + 6b2) = 0 (5 * 8b4 + 3b * 8b4 + 6b2 * 8b4) = 0 (40b4 + 24b5 + 48b6) = 0 Solving 40b4 + 24b5 + 48b6 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '8b4'. 8b4(5 + 3b + 6b2) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'b4' equal to zero and attempt to solve: Simplifying b4 = 0 Solving b4 = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b4 = 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 + 3b + 6b2)' equal to zero and attempt to solve: Simplifying 5 + 3b + 6b2 = 0 Solving 5 + 3b + 6b2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 0.5b + b2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 0.5b + -0.8333333333 + b2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 0.5b + b2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 0.5b + b2 = 0 + -0.8333333333 0.5b + b2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 0.5b + b2 = -0.8333333333 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 = -0.8333333333 + 0.0625 Reorder the terms: 0.0625 + 0.5b + b2 = -0.8333333333 + 0.0625 Combine like terms: -0.8333333333 + 0.0625 = -0.7708333333 0.0625 + 0.5b + b2 = -0.7708333333 Factor a perfect square on the left side: (b + 0.25)(b + 0.25) = -0.7708333333 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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