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Simplifying 6v2 + 12v + 52 = 0 Reorder the terms: 52 + 12v + 6v2 = 0 Solving 52 + 12v + 6v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(26 + 6v + 3v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(26 + 6v + 3v2)' equal to zero and attempt to solve: Simplifying 26 + 6v + 3v2 = 0 Solving 26 + 6v + 3v2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8.666666667 + 2v + v2 = 0 Move the constant term to the right: Add '-8.666666667' to each side of the equation. 8.666666667 + 2v + -8.666666667 + v2 = 0 + -8.666666667 Reorder the terms: 8.666666667 + -8.666666667 + 2v + v2 = 0 + -8.666666667 Combine like terms: 8.666666667 + -8.666666667 = 0.000000000 0.000000000 + 2v + v2 = 0 + -8.666666667 2v + v2 = 0 + -8.666666667 Combine like terms: 0 + -8.666666667 = -8.666666667 2v + v2 = -8.666666667 The v term is 2v. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2v + 1 + v2 = -8.666666667 + 1 Reorder the terms: 1 + 2v + v2 = -8.666666667 + 1 Combine like terms: -8.666666667 + 1 = -7.666666667 1 + 2v + v2 = -7.666666667 Factor a perfect square on the left side: (v + 1)(v + 1) = -7.666666667 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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