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Simplifying 7v2 + -1v + 12 = -3v2 + 6v Reorder the terms: 12 + -1v + 7v2 = -3v2 + 6v Reorder the terms: 12 + -1v + 7v2 = 6v + -3v2 Solving 12 + -1v + 7v2 = 6v + -3v2 Solving for variable 'v'. Reorder the terms: 12 + -1v + -6v + 7v2 + 3v2 = 6v + -3v2 + -6v + 3v2 Combine like terms: -1v + -6v = -7v 12 + -7v + 7v2 + 3v2 = 6v + -3v2 + -6v + 3v2 Combine like terms: 7v2 + 3v2 = 10v2 12 + -7v + 10v2 = 6v + -3v2 + -6v + 3v2 Reorder the terms: 12 + -7v + 10v2 = 6v + -6v + -3v2 + 3v2 Combine like terms: 6v + -6v = 0 12 + -7v + 10v2 = 0 + -3v2 + 3v2 12 + -7v + 10v2 = -3v2 + 3v2 Combine like terms: -3v2 + 3v2 = 0 12 + -7v + 10v2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.2 + -0.7v + v2 = 0.0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -0.7v + -1.2 + v2 = 0.0 + -1.2 Reorder the terms: 1.2 + -1.2 + -0.7v + v2 = 0.0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -0.7v + v2 = 0.0 + -1.2 -0.7v + v2 = 0.0 + -1.2 Combine like terms: 0.0 + -1.2 = -1.2 -0.7v + v2 = -1.2 The v term is -0.7v. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7v + 0.1225 + v2 = -1.2 + 0.1225 Reorder the terms: 0.1225 + -0.7v + v2 = -1.2 + 0.1225 Combine like terms: -1.2 + 0.1225 = -1.0775 0.1225 + -0.7v + v2 = -1.0775 Factor a perfect square on the left side: (v + -0.35)(v + -0.35) = -1.0775 Can't calculate square root of the right side. The solution to this equation could not be determined.
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