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Simplifying 6v(2 + -6v) + -3(v + 7) = 0 (2 * 6v + -6v * 6v) + -3(v + 7) = 0 (12v + -36v2) + -3(v + 7) = 0 Reorder the terms: 12v + -36v2 + -3(7 + v) = 0 12v + -36v2 + (7 * -3 + v * -3) = 0 12v + -36v2 + (-21 + -3v) = 0 Reorder the terms: -21 + 12v + -3v + -36v2 = 0 Combine like terms: 12v + -3v = 9v -21 + 9v + -36v2 = 0 Solving -21 + 9v + -36v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 3v + -12v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + 3v + -12v2)' equal to zero and attempt to solve: Simplifying -7 + 3v + -12v2 = 0 Solving -7 + 3v + -12v2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 0.5833333333 + -0.25v + v2 = 0 Move the constant term to the right: Add '-0.5833333333' to each side of the equation. 0.5833333333 + -0.25v + -0.5833333333 + v2 = 0 + -0.5833333333 Reorder the terms: 0.5833333333 + -0.5833333333 + -0.25v + v2 = 0 + -0.5833333333 Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000 0.0000000000 + -0.25v + v2 = 0 + -0.5833333333 -0.25v + v2 = 0 + -0.5833333333 Combine like terms: 0 + -0.5833333333 = -0.5833333333 -0.25v + v2 = -0.5833333333 The v term is -0.25v. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25v + 0.015625 + v2 = -0.5833333333 + 0.015625 Reorder the terms: 0.015625 + -0.25v + v2 = -0.5833333333 + 0.015625 Combine like terms: -0.5833333333 + 0.015625 = -0.5677083333 0.015625 + -0.25v + v2 = -0.5677083333 Factor a perfect square on the left side: (v + -0.125)(v + -0.125) = -0.5677083333 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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