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Simplifying 12v2 = -10v + -10 Reorder the terms: 12v2 = -10 + -10v Solving 12v2 = -10 + -10v Solving for variable 'v'. Reorder the terms: 10 + 10v + 12v2 = -10 + -10v + 10 + 10v Reorder the terms: 10 + 10v + 12v2 = -10 + 10 + -10v + 10v Combine like terms: -10 + 10 = 0 10 + 10v + 12v2 = 0 + -10v + 10v 10 + 10v + 12v2 = -10v + 10v Combine like terms: -10v + 10v = 0 10 + 10v + 12v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 5v + 6v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 5v + 6v2)' equal to zero and attempt to solve: Simplifying 5 + 5v + 6v2 = 0 Solving 5 + 5v + 6v2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 0.8333333333v + v2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 0.8333333333v + -0.8333333333 + v2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 0.8333333333v + v2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 0.8333333333v + v2 = 0 + -0.8333333333 0.8333333333v + v2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 0.8333333333v + v2 = -0.8333333333 The v term is 0.8333333333v. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333v + 0.1736111111 + v2 = -0.8333333333 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333v + v2 = -0.8333333333 + 0.1736111111 Combine like terms: -0.8333333333 + 0.1736111111 = -0.6597222222 0.1736111111 + 0.8333333333v + v2 = -0.6597222222 Factor a perfect square on the left side: (v + 0.4166666667)(v + 0.4166666667) = -0.6597222222 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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