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Simplifying 9b = 6b2 + 21 Reorder the terms: 9b = 21 + 6b2 Solving 9b = 21 + 6b2 Solving for variable 'b'. Reorder the terms: -21 + 9b + -6b2 = 21 + 6b2 + -21 + -6b2 Reorder the terms: -21 + 9b + -6b2 = 21 + -21 + 6b2 + -6b2 Combine like terms: 21 + -21 = 0 -21 + 9b + -6b2 = 0 + 6b2 + -6b2 -21 + 9b + -6b2 = 6b2 + -6b2 Combine like terms: 6b2 + -6b2 = 0 -21 + 9b + -6b2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 3b + -2b2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + 3b + -2b2)' equal to zero and attempt to solve: Simplifying -7 + 3b + -2b2 = 0 Solving -7 + 3b + -2b2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 3.5 + -1.5b + b2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -1.5b + -3.5 + b2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -1.5b + b2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -1.5b + b2 = 0 + -3.5 -1.5b + b2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -1.5b + b2 = -3.5 The b term is -1.5b. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5b + 0.5625 + b2 = -3.5 + 0.5625 Reorder the terms: 0.5625 + -1.5b + b2 = -3.5 + 0.5625 Combine like terms: -3.5 + 0.5625 = -2.9375 0.5625 + -1.5b + b2 = -2.9375 Factor a perfect square on the left side: (b + -0.75)(b + -0.75) = -2.9375 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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