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Simplifying 12v2 + 11v = 13 Reorder the terms: 11v + 12v2 = 13 Solving 11v + 12v2 = 13 Solving for variable 'v'. Reorder the terms: -13 + 11v + 12v2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 11v + 12v2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.083333333 + 0.9166666667v + v2 = 0 Move the constant term to the right: Add '1.083333333' to each side of the equation. -1.083333333 + 0.9166666667v + 1.083333333 + v2 = 0 + 1.083333333 Reorder the terms: -1.083333333 + 1.083333333 + 0.9166666667v + v2 = 0 + 1.083333333 Combine like terms: -1.083333333 + 1.083333333 = 0.000000000 0.000000000 + 0.9166666667v + v2 = 0 + 1.083333333 0.9166666667v + v2 = 0 + 1.083333333 Combine like terms: 0 + 1.083333333 = 1.083333333 0.9166666667v + v2 = 1.083333333 The v term is 0.9166666667v. Take half its coefficient (0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. 0.9166666667v + 0.2100694445 + v2 = 1.083333333 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667v + v2 = 1.083333333 + 0.2100694445 Combine like terms: 1.083333333 + 0.2100694445 = 1.2934027775 0.2100694445 + 0.9166666667v + v2 = 1.2934027775 Factor a perfect square on the left side: (v + 0.4583333334)(v + 0.4583333334) = 1.2934027775 Calculate the square root of the right side: 1.137278672 Break this problem into two subproblems by setting (v + 0.4583333334) equal to 1.137278672 and -1.137278672.Subproblem 1
v + 0.4583333334 = 1.137278672 Simplifying v + 0.4583333334 = 1.137278672 Reorder the terms: 0.4583333334 + v = 1.137278672 Solving 0.4583333334 + v = 1.137278672 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + v = 1.137278672 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + v = 1.137278672 + -0.4583333334 v = 1.137278672 + -0.4583333334 Combine like terms: 1.137278672 + -0.4583333334 = 0.6789453386 v = 0.6789453386 Simplifying v = 0.6789453386Subproblem 2
v + 0.4583333334 = -1.137278672 Simplifying v + 0.4583333334 = -1.137278672 Reorder the terms: 0.4583333334 + v = -1.137278672 Solving 0.4583333334 + v = -1.137278672 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + v = -1.137278672 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + v = -1.137278672 + -0.4583333334 v = -1.137278672 + -0.4583333334 Combine like terms: -1.137278672 + -0.4583333334 = -1.5956120054 v = -1.5956120054 Simplifying v = -1.5956120054Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.6789453386, -1.5956120054}
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