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Simplifying (-4v2 + 2v + -1) + (6v2 + 3v + 7) = 0 Reorder the terms: (-1 + 2v + -4v2) + (6v2 + 3v + 7) = 0 Remove parenthesis around (-1 + 2v + -4v2) -1 + 2v + -4v2 + (6v2 + 3v + 7) = 0 Reorder the terms: -1 + 2v + -4v2 + (7 + 3v + 6v2) = 0 Remove parenthesis around (7 + 3v + 6v2) -1 + 2v + -4v2 + 7 + 3v + 6v2 = 0 Reorder the terms: -1 + 7 + 2v + 3v + -4v2 + 6v2 = 0 Combine like terms: -1 + 7 = 6 6 + 2v + 3v + -4v2 + 6v2 = 0 Combine like terms: 2v + 3v = 5v 6 + 5v + -4v2 + 6v2 = 0 Combine like terms: -4v2 + 6v2 = 2v2 6 + 5v + 2v2 = 0 Solving 6 + 5v + 2v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 2.5v + v2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 2.5v + -3 + v2 = 0 + -3 Reorder the terms: 3 + -3 + 2.5v + v2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2.5v + v2 = 0 + -3 2.5v + v2 = 0 + -3 Combine like terms: 0 + -3 = -3 2.5v + v2 = -3 The v term is 2.5v. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5v + 1.5625 + v2 = -3 + 1.5625 Reorder the terms: 1.5625 + 2.5v + v2 = -3 + 1.5625 Combine like terms: -3 + 1.5625 = -1.4375 1.5625 + 2.5v + v2 = -1.4375 Factor a perfect square on the left side: (v + 1.25)(v + 1.25) = -1.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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