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Simplifying 11v2 + -11v + -17 = 0 Reorder the terms: -17 + -11v + 11v2 = 0 Solving -17 + -11v + 11v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.545454545 + -1v + v2 = 0 Move the constant term to the right: Add '1.545454545' to each side of the equation. -1.545454545 + -1v + 1.545454545 + v2 = 0 + 1.545454545 Reorder the terms: -1.545454545 + 1.545454545 + -1v + v2 = 0 + 1.545454545 Combine like terms: -1.545454545 + 1.545454545 = 0.000000000 0.000000000 + -1v + v2 = 0 + 1.545454545 -1v + v2 = 0 + 1.545454545 Combine like terms: 0 + 1.545454545 = 1.545454545 -1v + v2 = 1.545454545 The v term is -1v. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1v + 0.25 + v2 = 1.545454545 + 0.25 Reorder the terms: 0.25 + -1v + v2 = 1.545454545 + 0.25 Combine like terms: 1.545454545 + 0.25 = 1.795454545 0.25 + -1v + v2 = 1.795454545 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 1.795454545 Calculate the square root of the right side: 1.339945725 Break this problem into two subproblems by setting (v + -0.5) equal to 1.339945725 and -1.339945725.Subproblem 1
v + -0.5 = 1.339945725 Simplifying v + -0.5 = 1.339945725 Reorder the terms: -0.5 + v = 1.339945725 Solving -0.5 + v = 1.339945725 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = 1.339945725 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 1.339945725 + 0.5 v = 1.339945725 + 0.5 Combine like terms: 1.339945725 + 0.5 = 1.839945725 v = 1.839945725 Simplifying v = 1.839945725Subproblem 2
v + -0.5 = -1.339945725 Simplifying v + -0.5 = -1.339945725 Reorder the terms: -0.5 + v = -1.339945725 Solving -0.5 + v = -1.339945725 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = -1.339945725 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -1.339945725 + 0.5 v = -1.339945725 + 0.5 Combine like terms: -1.339945725 + 0.5 = -0.839945725 v = -0.839945725 Simplifying v = -0.839945725Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.839945725, -0.839945725}
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