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Simplifying 2b2 + 4b + 28 = 0 Reorder the terms: 28 + 4b + 2b2 = 0 Solving 28 + 4b + 2b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 2b + b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + 2b + b2)' equal to zero and attempt to solve: Simplifying 14 + 2b + b2 = 0 Solving 14 + 2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 2b + -14 + b2 = 0 + -14 Reorder the terms: 14 + -14 + 2b + b2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 2b + b2 = 0 + -14 2b + b2 = 0 + -14 Combine like terms: 0 + -14 = -14 2b + b2 = -14 The b term is 2b. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2b + 1 + b2 = -14 + 1 Reorder the terms: 1 + 2b + b2 = -14 + 1 Combine like terms: -14 + 1 = -13 1 + 2b + b2 = -13 Factor a perfect square on the left side: (b + 1)(b + 1) = -13 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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