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Simplifying -12v2 + 8v + -16 = 0 Reorder the terms: -16 + 8v + -12v2 = 0 Solving -16 + 8v + -12v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 2v + -3v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + 2v + -3v2)' equal to zero and attempt to solve: Simplifying -4 + 2v + -3v2 = 0 Solving -4 + 2v + -3v2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.333333333 + -0.6666666667v + v2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -0.6666666667v + -1.333333333 + v2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -0.6666666667v + v2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -0.6666666667v + v2 = 0 + -1.333333333 -0.6666666667v + v2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -0.6666666667v + v2 = -1.333333333 The v term is -0.6666666667v. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667v + 0.1111111112 + v2 = -1.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667v + v2 = -1.333333333 + 0.1111111112 Combine like terms: -1.333333333 + 0.1111111112 = -1.2222222218 0.1111111112 + -0.6666666667v + v2 = -1.2222222218 Factor a perfect square on the left side: (v + -0.3333333334)(v + -0.3333333334) = -1.2222222218 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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