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Simplifying 12v2 + 12v + 6 = 0 Reorder the terms: 6 + 12v + 12v2 = 0 Solving 6 + 12v + 12v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '6'. 6(1 + 2v + 2v2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(1 + 2v + 2v2)' equal to zero and attempt to solve: Simplifying 1 + 2v + 2v2 = 0 Solving 1 + 2v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + v + v2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + v + -0.5 + v2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + v + v2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v + v2 = 0 + -0.5 v + v2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 v + v2 = -0.5 The v term is v. 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. + 0.25 + v2 = -0.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + v2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 1.25 + v2 = -0.25 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = -0.25 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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