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Simplifying 36v2 + -12v + 20 = 0 Reorder the terms: 20 + -12v + 36v2 = 0 Solving 20 + -12v + 36v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -3v + 9v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -3v + 9v2)' equal to zero and attempt to solve: Simplifying 5 + -3v + 9v2 = 0 Solving 5 + -3v + 9v2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + -0.3333333333v + v2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + -0.3333333333v + -0.5555555556 + v2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + -0.3333333333v + v2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + -0.3333333333v + v2 = 0 + -0.5555555556 -0.3333333333v + v2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 -0.3333333333v + v2 = -0.5555555556 The v term is -0.3333333333v. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333v + 0.02777777779 + v2 = -0.5555555556 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333v + v2 = -0.5555555556 + 0.02777777779 Combine like terms: -0.5555555556 + 0.02777777779 = -0.52777777781 0.02777777779 + -0.3333333333v + v2 = -0.52777777781 Factor a perfect square on the left side: (v + -0.1666666667)(v + -0.1666666667) = -0.52777777781 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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