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Simplifying (-3v2 + 6v + -2) + (v2 + 5v + 4) = 0 Reorder the terms: (-2 + 6v + -3v2) + (v2 + 5v + 4) = 0 Remove parenthesis around (-2 + 6v + -3v2) -2 + 6v + -3v2 + (v2 + 5v + 4) = 0 Reorder the terms: -2 + 6v + -3v2 + (4 + 5v + v2) = 0 Remove parenthesis around (4 + 5v + v2) -2 + 6v + -3v2 + 4 + 5v + v2 = 0 Reorder the terms: -2 + 4 + 6v + 5v + -3v2 + v2 = 0 Combine like terms: -2 + 4 = 2 2 + 6v + 5v + -3v2 + v2 = 0 Combine like terms: 6v + 5v = 11v 2 + 11v + -3v2 + v2 = 0 Combine like terms: -3v2 + v2 = -2v2 2 + 11v + -2v2 = 0 Solving 2 + 11v + -2v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + -5.5v + v2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -5.5v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + -5.5v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5.5v + v2 = 0 + 1 -5.5v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 -5.5v + v2 = 1 The v term is -5.5v. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5v + 7.5625 + v2 = 1 + 7.5625 Reorder the terms: 7.5625 + -5.5v + v2 = 1 + 7.5625 Combine like terms: 1 + 7.5625 = 8.5625 7.5625 + -5.5v + v2 = 8.5625 Factor a perfect square on the left side: (v + -2.75)(v + -2.75) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (v + -2.75) equal to 2.926174978 and -2.926174978.Subproblem 1
v + -2.75 = 2.926174978 Simplifying v + -2.75 = 2.926174978 Reorder the terms: -2.75 + v = 2.926174978 Solving -2.75 + v = 2.926174978 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + v = 2.926174978 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + v = 2.926174978 + 2.75 v = 2.926174978 + 2.75 Combine like terms: 2.926174978 + 2.75 = 5.676174978 v = 5.676174978 Simplifying v = 5.676174978Subproblem 2
v + -2.75 = -2.926174978 Simplifying v + -2.75 = -2.926174978 Reorder the terms: -2.75 + v = -2.926174978 Solving -2.75 + v = -2.926174978 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + v = -2.926174978 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + v = -2.926174978 + 2.75 v = -2.926174978 + 2.75 Combine like terms: -2.926174978 + 2.75 = -0.176174978 v = -0.176174978 Simplifying v = -0.176174978Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.676174978, -0.176174978}
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