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Simplifying (-3v2 + -4v + 4) + -1(-3v2 + 4v + -2) + (-7v2 + -2v + -4) = 0 Reorder the terms: (4 + -4v + -3v2) + -1(-3v2 + 4v + -2) + (-7v2 + -2v + -4) = 0 Remove parenthesis around (4 + -4v + -3v2) 4 + -4v + -3v2 + -1(-3v2 + 4v + -2) + (-7v2 + -2v + -4) = 0 Reorder the terms: 4 + -4v + -3v2 + -1(-2 + 4v + -3v2) + (-7v2 + -2v + -4) = 0 4 + -4v + -3v2 + (-2 * -1 + 4v * -1 + -3v2 * -1) + (-7v2 + -2v + -4) = 0 4 + -4v + -3v2 + (2 + -4v + 3v2) + (-7v2 + -2v + -4) = 0 Reorder the terms: 4 + -4v + -3v2 + 2 + -4v + 3v2 + (-4 + -2v + -7v2) = 0 Remove parenthesis around (-4 + -2v + -7v2) 4 + -4v + -3v2 + 2 + -4v + 3v2 + -4 + -2v + -7v2 = 0 Reorder the terms: 4 + 2 + -4 + -4v + -4v + -2v + -3v2 + 3v2 + -7v2 = 0 Combine like terms: 4 + 2 = 6 6 + -4 + -4v + -4v + -2v + -3v2 + 3v2 + -7v2 = 0 Combine like terms: 6 + -4 = 2 2 + -4v + -4v + -2v + -3v2 + 3v2 + -7v2 = 0 Combine like terms: -4v + -4v = -8v 2 + -8v + -2v + -3v2 + 3v2 + -7v2 = 0 Combine like terms: -8v + -2v = -10v 2 + -10v + -3v2 + 3v2 + -7v2 = 0 Combine like terms: -3v2 + 3v2 = 0 2 + -10v + 0 + -7v2 = 0 2 + -10v + -7v2 = 0 Solving 2 + -10v + -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'. -0.2857142857 + 1.428571429v + v2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 1.428571429v + 0.2857142857 + v2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 1.428571429v + v2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 1.428571429v + v2 = 0 + 0.2857142857 1.428571429v + v2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 1.428571429v + v2 = 0.2857142857 The v term is 1.428571429v. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429v + 0.5102040819 + v2 = 0.2857142857 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429v + v2 = 0.2857142857 + 0.5102040819 Combine like terms: 0.2857142857 + 0.5102040819 = 0.7959183676 0.5102040819 + 1.428571429v + v2 = 0.7959183676 Factor a perfect square on the left side: (v + 0.7142857145)(v + 0.7142857145) = 0.7959183676 Calculate the square root of the right side: 0.892142571 Break this problem into two subproblems by setting (v + 0.7142857145) equal to 0.892142571 and -0.892142571.Subproblem 1
v + 0.7142857145 = 0.892142571 Simplifying v + 0.7142857145 = 0.892142571 Reorder the terms: 0.7142857145 + v = 0.892142571 Solving 0.7142857145 + v = 0.892142571 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + v = 0.892142571 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + v = 0.892142571 + -0.7142857145 v = 0.892142571 + -0.7142857145 Combine like terms: 0.892142571 + -0.7142857145 = 0.1778568565 v = 0.1778568565 Simplifying v = 0.1778568565Subproblem 2
v + 0.7142857145 = -0.892142571 Simplifying v + 0.7142857145 = -0.892142571 Reorder the terms: 0.7142857145 + v = -0.892142571 Solving 0.7142857145 + v = -0.892142571 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + v = -0.892142571 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + v = -0.892142571 + -0.7142857145 v = -0.892142571 + -0.7142857145 Combine like terms: -0.892142571 + -0.7142857145 = -1.6064282855 v = -1.6064282855 Simplifying v = -1.6064282855Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.1778568565, -1.6064282855}
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