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Simplifying (6 + -4)(8b2 + -5b + 6) = 0 Combine like terms: 6 + -4 = 2 (2)(8b2 + -5b + 6) = 0 Reorder the terms: 2(6 + -5b + 8b2) = 0 (6 * 2 + -5b * 2 + 8b2 * 2) = 0 (12 + -10b + 16b2) = 0 Solving 12 + -10b + 16b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -5b + 8b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -5b + 8b2)' equal to zero and attempt to solve: Simplifying 6 + -5b + 8b2 = 0 Solving 6 + -5b + 8b2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.75 + -0.625b + b2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -0.625b + -0.75 + b2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -0.625b + b2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -0.625b + b2 = 0 + -0.75 -0.625b + b2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -0.625b + b2 = -0.75 The b term is -0.625b. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625b + 0.09765625 + b2 = -0.75 + 0.09765625 Reorder the terms: 0.09765625 + -0.625b + b2 = -0.75 + 0.09765625 Combine like terms: -0.75 + 0.09765625 = -0.65234375 0.09765625 + -0.625b + b2 = -0.65234375 Factor a perfect square on the left side: (b + -0.3125)(b + -0.3125) = -0.65234375 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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