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Simplifying 5v2 + 6v + 7 = v2 + -4v Reorder the terms: 7 + 6v + 5v2 = v2 + -4v Reorder the terms: 7 + 6v + 5v2 = -4v + v2 Solving 7 + 6v + 5v2 = -4v + v2 Solving for variable 'v'. Reorder the terms: 7 + 6v + 4v + 5v2 + -1v2 = -4v + v2 + 4v + -1v2 Combine like terms: 6v + 4v = 10v 7 + 10v + 5v2 + -1v2 = -4v + v2 + 4v + -1v2 Combine like terms: 5v2 + -1v2 = 4v2 7 + 10v + 4v2 = -4v + v2 + 4v + -1v2 Reorder the terms: 7 + 10v + 4v2 = -4v + 4v + v2 + -1v2 Combine like terms: -4v + 4v = 0 7 + 10v + 4v2 = 0 + v2 + -1v2 7 + 10v + 4v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 7 + 10v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 2.5v + v2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 2.5v + -1.75 + v2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 2.5v + v2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 2.5v + v2 = 0 + -1.75 2.5v + v2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 2.5v + v2 = -1.75 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 = -1.75 + 1.5625 Reorder the terms: 1.5625 + 2.5v + v2 = -1.75 + 1.5625 Combine like terms: -1.75 + 1.5625 = -0.1875 1.5625 + 2.5v + v2 = -0.1875 Factor a perfect square on the left side: (v + 1.25)(v + 1.25) = -0.1875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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