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Simplifying 2v2 + 6v + 61 = (v + 7) Reorder the terms: 61 + 6v + 2v2 = (v + 7) Reorder the terms: 61 + 6v + 2v2 = (7 + v) Remove parenthesis around (7 + v) 61 + 6v + 2v2 = 7 + v Solving 61 + 6v + 2v2 = 7 + v Solving for variable 'v'. Reorder the terms: 61 + -7 + 6v + -1v + 2v2 = 7 + v + -7 + -1v Combine like terms: 61 + -7 = 54 54 + 6v + -1v + 2v2 = 7 + v + -7 + -1v Combine like terms: 6v + -1v = 5v 54 + 5v + 2v2 = 7 + v + -7 + -1v Reorder the terms: 54 + 5v + 2v2 = 7 + -7 + v + -1v Combine like terms: 7 + -7 = 0 54 + 5v + 2v2 = 0 + v + -1v 54 + 5v + 2v2 = v + -1v Combine like terms: v + -1v = 0 54 + 5v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 27 + 2.5v + v2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + 2.5v + -27 + v2 = 0 + -27 Reorder the terms: 27 + -27 + 2.5v + v2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 2.5v + v2 = 0 + -27 2.5v + v2 = 0 + -27 Combine like terms: 0 + -27 = -27 2.5v + v2 = -27 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 = -27 + 1.5625 Reorder the terms: 1.5625 + 2.5v + v2 = -27 + 1.5625 Combine like terms: -27 + 1.5625 = -25.4375 1.5625 + 2.5v + v2 = -25.4375 Factor a perfect square on the left side: (v + 1.25)(v + 1.25) = -25.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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