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Simplifying 4b2 + 4bc + 16c2 = 0 Reorder the terms: 4bc + 4b2 + 16c2 = 0 Solving 4bc + 4b2 + 16c2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4'. 4(bc + b2 + 4c2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(bc + b2 + 4c2)' equal to zero and attempt to solve: Simplifying bc + b2 + 4c2 = 0 Solving bc + b2 + 4c2 = 0 Begin completing the square. Move the constant term to the right: Add '-4c2' to each side of the equation. bc + b2 + 4c2 + -4c2 = 0 + -4c2 Combine like terms: 4c2 + -4c2 = 0 bc + b2 + 0 = 0 + -4c2 bc + b2 = 0 + -4c2 Remove the zero: bc + b2 = -4c2 The b term is bc. Take half its coefficient (0.5c). Square it (0.25c2) and add it to both sides. Add '0.25c2' to each side of the equation. bc + b2 + 0.25c2 = -4c2 + 0.25c2 Combine like terms: -4c2 + 0.25c2 = -3.75c2 bc + b2 + 0.25c2 = -3.75c2 Factor a perfect square on the left side: (b + 0.5c)(b + 0.5c) = -3.75c2 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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