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Simplifying v + -4 = 2v2 + -12v + 19 Reorder the terms: -4 + v = 2v2 + -12v + 19 Reorder the terms: -4 + v = 19 + -12v + 2v2 Solving -4 + v = 19 + -12v + 2v2 Solving for variable 'v'. Reorder the terms: -4 + -19 + v + 12v + -2v2 = 19 + -12v + 2v2 + -19 + 12v + -2v2 Combine like terms: -4 + -19 = -23 -23 + v + 12v + -2v2 = 19 + -12v + 2v2 + -19 + 12v + -2v2 Combine like terms: v + 12v = 13v -23 + 13v + -2v2 = 19 + -12v + 2v2 + -19 + 12v + -2v2 Reorder the terms: -23 + 13v + -2v2 = 19 + -19 + -12v + 12v + 2v2 + -2v2 Combine like terms: 19 + -19 = 0 -23 + 13v + -2v2 = 0 + -12v + 12v + 2v2 + -2v2 -23 + 13v + -2v2 = -12v + 12v + 2v2 + -2v2 Combine like terms: -12v + 12v = 0 -23 + 13v + -2v2 = 0 + 2v2 + -2v2 -23 + 13v + -2v2 = 2v2 + -2v2 Combine like terms: 2v2 + -2v2 = 0 -23 + 13v + -2v2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 11.5 + -6.5v + v2 = 0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + -6.5v + -11.5 + v2 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + -6.5v + v2 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + -6.5v + v2 = 0 + -11.5 -6.5v + v2 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 -6.5v + v2 = -11.5 The v term is -6.5v. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5v + 10.5625 + v2 = -11.5 + 10.5625 Reorder the terms: 10.5625 + -6.5v + v2 = -11.5 + 10.5625 Combine like terms: -11.5 + 10.5625 = -0.9375 10.5625 + -6.5v + v2 = -0.9375 Factor a perfect square on the left side: (v + -3.25)(v + -3.25) = -0.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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