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Simplifying 9 = 6v + -9v2 Solving 9 = 6v + -9v2 Solving for variable 'v'. Reorder the terms: 9 + -6v + 9v2 = 6v + -6v + -9v2 + 9v2 Combine like terms: 6v + -6v = 0 9 + -6v + 9v2 = 0 + -9v2 + 9v2 9 + -6v + 9v2 = -9v2 + 9v2 Combine like terms: -9v2 + 9v2 = 0 9 + -6v + 9v2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -2v + 3v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -2v + 3v2)' equal to zero and attempt to solve: Simplifying 3 + -2v + 3v2 = 0 Solving 3 + -2v + 3v2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -0.6666666667v + v2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.6666666667v + -1 + v2 = 0 + -1 Reorder the terms: 1 + -1 + -0.6666666667v + v2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.6666666667v + v2 = 0 + -1 -0.6666666667v + v2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.6666666667v + v2 = -1 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 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667v + v2 = -1 + 0.1111111112 Combine like terms: -1 + 0.1111111112 = -0.8888888888 0.1111111112 + -0.6666666667v + v2 = -0.8888888888 Factor a perfect square on the left side: (v + -0.3333333334)(v + -0.3333333334) = -0.8888888888 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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