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Simplifying 2b2 = 2b + -54 Reorder the terms: 2b2 = -54 + 2b Solving 2b2 = -54 + 2b Solving for variable 'b'. Reorder the terms: 54 + -2b + 2b2 = -54 + 2b + 54 + -2b Reorder the terms: 54 + -2b + 2b2 = -54 + 54 + 2b + -2b Combine like terms: -54 + 54 = 0 54 + -2b + 2b2 = 0 + 2b + -2b 54 + -2b + 2b2 = 2b + -2b Combine like terms: 2b + -2b = 0 54 + -2b + 2b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -1b + b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + -1b + b2)' equal to zero and attempt to solve: Simplifying 27 + -1b + b2 = 0 Solving 27 + -1b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -1b + -27 + b2 = 0 + -27 Reorder the terms: 27 + -27 + -1b + b2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -1b + b2 = 0 + -27 -1b + b2 = 0 + -27 Combine like terms: 0 + -27 = -27 -1b + b2 = -27 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 = -27 + 0.25 Reorder the terms: 0.25 + -1b + b2 = -27 + 0.25 Combine like terms: -27 + 0.25 = -26.75 0.25 + -1b + b2 = -26.75 Factor a perfect square on the left side: (b + -0.5)(b + -0.5) = -26.75 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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