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Simplifying 38b2 + 38b + 12 = 0 Reorder the terms: 12 + 38b + 38b2 = 0 Solving 12 + 38b + 38b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 19b + 19b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + 19b + 19b2)' equal to zero and attempt to solve: Simplifying 6 + 19b + 19b2 = 0 Solving 6 + 19b + 19b2 = 0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. 0.3157894737 + b + b2 = 0 Move the constant term to the right: Add '-0.3157894737' to each side of the equation. 0.3157894737 + b + -0.3157894737 + b2 = 0 + -0.3157894737 Reorder the terms: 0.3157894737 + -0.3157894737 + b + b2 = 0 + -0.3157894737 Combine like terms: 0.3157894737 + -0.3157894737 = 0.0000000000 0.0000000000 + b + b2 = 0 + -0.3157894737 b + b2 = 0 + -0.3157894737 Combine like terms: 0 + -0.3157894737 = -0.3157894737 b + b2 = -0.3157894737 The b term is b. 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. + 0.25 + b2 = -0.3157894737 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + b2 = -0.3157894737 + 0.25 Combine like terms: -0.3157894737 + 0.25 = -0.0657894737 1.25 + b2 = -0.0657894737 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = -0.0657894737 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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