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Simplifying 6b + -6b2 = 8 Solving 6b + -6b2 = 8 Solving for variable 'b'. Reorder the terms: -8 + 6b + -6b2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 6b + -6b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 3b + -3b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 3b + -3b2)' equal to zero and attempt to solve: Simplifying -4 + 3b + -3b2 = 0 Solving -4 + 3b + -3b2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.333333333 + -1b + b2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -1b + -1.333333333 + b2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -1b + b2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -1b + b2 = 0 + -1.333333333 -1b + b2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -1b + b2 = -1.333333333 The b term is -1b. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1b + 0.25 + b2 = -1.333333333 + 0.25 Reorder the terms: 0.25 + -1b + b2 = -1.333333333 + 0.25 Combine like terms: -1.333333333 + 0.25 = -1.083333333 0.25 + -1b + b2 = -1.083333333 Factor a perfect square on the left side: (b + -0.5)(b + -0.5) = -1.083333333 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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