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Simplifying 2b2 + -2b = -12 Reorder the terms: -2b + 2b2 = -12 Solving -2b + 2b2 = -12 Solving for variable 'b'. Reorder the terms: 12 + -2b + 2b2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -2b + 2b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -1b + b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -1b + b2)' equal to zero and attempt to solve: Simplifying 6 + -1b + b2 = 0 Solving 6 + -1b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -1b + -6 + b2 = 0 + -6 Reorder the terms: 6 + -6 + -1b + b2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1b + b2 = 0 + -6 -1b + b2 = 0 + -6 Combine like terms: 0 + -6 = -6 -1b + b2 = -6 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 = -6 + 0.25 Reorder the terms: 0.25 + -1b + b2 = -6 + 0.25 Combine like terms: -6 + 0.25 = -5.75 0.25 + -1b + b2 = -5.75 Factor a perfect square on the left side: (b + -0.5)(b + -0.5) = -5.75 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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