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Simplifying 6b2 + -20b + 62 = 0 Reorder the terms: 62 + -20b + 6b2 = 0 Solving 62 + -20b + 6b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(31 + -10b + 3b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(31 + -10b + 3b2)' equal to zero and attempt to solve: Simplifying 31 + -10b + 3b2 = 0 Solving 31 + -10b + 3b2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10.33333333 + -3.333333333b + b2 = 0 Move the constant term to the right: Add '-10.33333333' to each side of the equation. 10.33333333 + -3.333333333b + -10.33333333 + b2 = 0 + -10.33333333 Reorder the terms: 10.33333333 + -10.33333333 + -3.333333333b + b2 = 0 + -10.33333333 Combine like terms: 10.33333333 + -10.33333333 = 0.00000000 0.00000000 + -3.333333333b + b2 = 0 + -10.33333333 -3.333333333b + b2 = 0 + -10.33333333 Combine like terms: 0 + -10.33333333 = -10.33333333 -3.333333333b + b2 = -10.33333333 The b term is -3.333333333b. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333b + 2.777777779 + b2 = -10.33333333 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333b + b2 = -10.33333333 + 2.777777779 Combine like terms: -10.33333333 + 2.777777779 = -7.555555551 2.777777779 + -3.333333333b + b2 = -7.555555551 Factor a perfect square on the left side: (b + -1.666666667)(b + -1.666666667) = -7.555555551 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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