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Simplifying (3v2 + 7v + 9) + (4v2 + 7v + 2) = 0 Reorder the terms: (9 + 7v + 3v2) + (4v2 + 7v + 2) = 0 Remove parenthesis around (9 + 7v + 3v2) 9 + 7v + 3v2 + (4v2 + 7v + 2) = 0 Reorder the terms: 9 + 7v + 3v2 + (2 + 7v + 4v2) = 0 Remove parenthesis around (2 + 7v + 4v2) 9 + 7v + 3v2 + 2 + 7v + 4v2 = 0 Reorder the terms: 9 + 2 + 7v + 7v + 3v2 + 4v2 = 0 Combine like terms: 9 + 2 = 11 11 + 7v + 7v + 3v2 + 4v2 = 0 Combine like terms: 7v + 7v = 14v 11 + 14v + 3v2 + 4v2 = 0 Combine like terms: 3v2 + 4v2 = 7v2 11 + 14v + 7v2 = 0 Solving 11 + 14v + 7v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.571428571 + 2v + v2 = 0 Move the constant term to the right: Add '-1.571428571' to each side of the equation. 1.571428571 + 2v + -1.571428571 + v2 = 0 + -1.571428571 Reorder the terms: 1.571428571 + -1.571428571 + 2v + v2 = 0 + -1.571428571 Combine like terms: 1.571428571 + -1.571428571 = 0.000000000 0.000000000 + 2v + v2 = 0 + -1.571428571 2v + v2 = 0 + -1.571428571 Combine like terms: 0 + -1.571428571 = -1.571428571 2v + v2 = -1.571428571 The v term is 2v. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2v + 1 + v2 = -1.571428571 + 1 Reorder the terms: 1 + 2v + v2 = -1.571428571 + 1 Combine like terms: -1.571428571 + 1 = -0.571428571 1 + 2v + v2 = -0.571428571 Factor a perfect square on the left side: (v + 1)(v + 1) = -0.571428571 Can't calculate square root of the right side. The solution to this equation could not be determined.
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