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Simplifying 9v2 + -7v + -12 = 0 Reorder the terms: -12 + -7v + 9v2 = 0 Solving -12 + -7v + 9v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.333333333 + -0.7777777778v + v2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -0.7777777778v + 1.333333333 + v2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -0.7777777778v + v2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -0.7777777778v + v2 = 0 + 1.333333333 -0.7777777778v + v2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -0.7777777778v + v2 = 1.333333333 The v term is -0.7777777778v. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778v + 0.1512345679 + v2 = 1.333333333 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778v + v2 = 1.333333333 + 0.1512345679 Combine like terms: 1.333333333 + 0.1512345679 = 1.4845679009 0.1512345679 + -0.7777777778v + v2 = 1.4845679009 Factor a perfect square on the left side: (v + -0.3888888889)(v + -0.3888888889) = 1.4845679009 Calculate the square root of the right side: 1.218428455 Break this problem into two subproblems by setting (v + -0.3888888889) equal to 1.218428455 and -1.218428455.Subproblem 1
v + -0.3888888889 = 1.218428455 Simplifying v + -0.3888888889 = 1.218428455 Reorder the terms: -0.3888888889 + v = 1.218428455 Solving -0.3888888889 + v = 1.218428455 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + v = 1.218428455 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + v = 1.218428455 + 0.3888888889 v = 1.218428455 + 0.3888888889 Combine like terms: 1.218428455 + 0.3888888889 = 1.6073173439 v = 1.6073173439 Simplifying v = 1.6073173439Subproblem 2
v + -0.3888888889 = -1.218428455 Simplifying v + -0.3888888889 = -1.218428455 Reorder the terms: -0.3888888889 + v = -1.218428455 Solving -0.3888888889 + v = -1.218428455 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + v = -1.218428455 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + v = -1.218428455 + 0.3888888889 v = -1.218428455 + 0.3888888889 Combine like terms: -1.218428455 + 0.3888888889 = -0.8295395661 v = -0.8295395661 Simplifying v = -0.8295395661Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.6073173439, -0.8295395661}
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