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Simplifying 2v2 + 9v + -8 + 11v2 + -6v + 6 + v + -1 = 0 Reorder the terms: -8 + 6 + -1 + 9v + -6v + v + 2v2 + 11v2 = 0 Combine like terms: -8 + 6 = -2 -2 + -1 + 9v + -6v + v + 2v2 + 11v2 = 0 Combine like terms: -2 + -1 = -3 -3 + 9v + -6v + v + 2v2 + 11v2 = 0 Combine like terms: 9v + -6v = 3v -3 + 3v + v + 2v2 + 11v2 = 0 Combine like terms: 3v + v = 4v -3 + 4v + 2v2 + 11v2 = 0 Combine like terms: 2v2 + 11v2 = 13v2 -3 + 4v + 13v2 = 0 Solving -3 + 4v + 13v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.2307692308 + 0.3076923077v + v2 = 0 Move the constant term to the right: Add '0.2307692308' to each side of the equation. -0.2307692308 + 0.3076923077v + 0.2307692308 + v2 = 0 + 0.2307692308 Reorder the terms: -0.2307692308 + 0.2307692308 + 0.3076923077v + v2 = 0 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + 0.3076923077v + v2 = 0 + 0.2307692308 0.3076923077v + v2 = 0 + 0.2307692308 Combine like terms: 0 + 0.2307692308 = 0.2307692308 0.3076923077v + v2 = 0.2307692308 The v term is 0.3076923077v. Take half its coefficient (0.1538461539). Square it (0.02366863907) and add it to both sides. Add '0.02366863907' to each side of the equation. 0.3076923077v + 0.02366863907 + v2 = 0.2307692308 + 0.02366863907 Reorder the terms: 0.02366863907 + 0.3076923077v + v2 = 0.2307692308 + 0.02366863907 Combine like terms: 0.2307692308 + 0.02366863907 = 0.25443786987 0.02366863907 + 0.3076923077v + v2 = 0.25443786987 Factor a perfect square on the left side: (v + 0.1538461539)(v + 0.1538461539) = 0.25443786987 Calculate the square root of the right side: 0.504418348 Break this problem into two subproblems by setting (v + 0.1538461539) equal to 0.504418348 and -0.504418348.Subproblem 1
v + 0.1538461539 = 0.504418348 Simplifying v + 0.1538461539 = 0.504418348 Reorder the terms: 0.1538461539 + v = 0.504418348 Solving 0.1538461539 + v = 0.504418348 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.1538461539' to each side of the equation. 0.1538461539 + -0.1538461539 + v = 0.504418348 + -0.1538461539 Combine like terms: 0.1538461539 + -0.1538461539 = 0.0000000000 0.0000000000 + v = 0.504418348 + -0.1538461539 v = 0.504418348 + -0.1538461539 Combine like terms: 0.504418348 + -0.1538461539 = 0.3505721941 v = 0.3505721941 Simplifying v = 0.3505721941Subproblem 2
v + 0.1538461539 = -0.504418348 Simplifying v + 0.1538461539 = -0.504418348 Reorder the terms: 0.1538461539 + v = -0.504418348 Solving 0.1538461539 + v = -0.504418348 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.1538461539' to each side of the equation. 0.1538461539 + -0.1538461539 + v = -0.504418348 + -0.1538461539 Combine like terms: 0.1538461539 + -0.1538461539 = 0.0000000000 0.0000000000 + v = -0.504418348 + -0.1538461539 v = -0.504418348 + -0.1538461539 Combine like terms: -0.504418348 + -0.1538461539 = -0.6582645019 v = -0.6582645019 Simplifying v = -0.6582645019Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.3505721941, -0.6582645019}
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