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Simplifying 0 = 0.06v2 + 1.1v + -200 Reorder the terms: 0 = -200 + 1.1v + 0.06v2 Solving 0 = -200 + 1.1v + 0.06v2 Solving for variable 'v'. Combine like terms: 0 + 200 = 200 200 + -1.1v + -0.06v2 = -200 + 1.1v + 0.06v2 + 200 + -1.1v + -0.06v2 Reorder the terms: 200 + -1.1v + -0.06v2 = -200 + 200 + 1.1v + -1.1v + 0.06v2 + -0.06v2 Combine like terms: -200 + 200 = 0 200 + -1.1v + -0.06v2 = 0 + 1.1v + -1.1v + 0.06v2 + -0.06v2 200 + -1.1v + -0.06v2 = 1.1v + -1.1v + 0.06v2 + -0.06v2 Combine like terms: 1.1v + -1.1v = 0.0 200 + -1.1v + -0.06v2 = 0.0 + 0.06v2 + -0.06v2 200 + -1.1v + -0.06v2 = 0.06v2 + -0.06v2 Combine like terms: 0.06v2 + -0.06v2 = 0.00 200 + -1.1v + -0.06v2 = 0.00 Begin completing the square. Divide all terms by -0.06 the coefficient of the squared term: Divide each side by '-0.06'. -3333.333333 + 18.33333333v + v2 = 0 Move the constant term to the right: Add '3333.333333' to each side of the equation. -3333.333333 + 18.33333333v + 3333.333333 + v2 = 0 + 3333.333333 Reorder the terms: -3333.333333 + 3333.333333 + 18.33333333v + v2 = 0 + 3333.333333 Combine like terms: -3333.333333 + 3333.333333 = 0.000000 0.000000 + 18.33333333v + v2 = 0 + 3333.333333 18.33333333v + v2 = 0 + 3333.333333 Combine like terms: 0 + 3333.333333 = 3333.333333 18.33333333v + v2 = 3333.333333 The v term is 18.33333333v. Take half its coefficient (9.166666665). Square it (84.02777775) and add it to both sides. Add '84.02777775' to each side of the equation. 18.33333333v + 84.02777775 + v2 = 3333.333333 + 84.02777775 Reorder the terms: 84.02777775 + 18.33333333v + v2 = 3333.333333 + 84.02777775 Combine like terms: 3333.333333 + 84.02777775 = 3417.36111075 84.02777775 + 18.33333333v + v2 = 3417.36111075 Factor a perfect square on the left side: (v + 9.166666665)(v + 9.166666665) = 3417.36111075 Calculate the square root of the right side: 58.458199688 Break this problem into two subproblems by setting (v + 9.166666665) equal to 58.458199688 and -58.458199688.Subproblem 1
v + 9.166666665 = 58.458199688 Simplifying v + 9.166666665 = 58.458199688 Reorder the terms: 9.166666665 + v = 58.458199688 Solving 9.166666665 + v = 58.458199688 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-9.166666665' to each side of the equation. 9.166666665 + -9.166666665 + v = 58.458199688 + -9.166666665 Combine like terms: 9.166666665 + -9.166666665 = 0.000000000 0.000000000 + v = 58.458199688 + -9.166666665 v = 58.458199688 + -9.166666665 Combine like terms: 58.458199688 + -9.166666665 = 49.291533023 v = 49.291533023 Simplifying v = 49.291533023Subproblem 2
v + 9.166666665 = -58.458199688 Simplifying v + 9.166666665 = -58.458199688 Reorder the terms: 9.166666665 + v = -58.458199688 Solving 9.166666665 + v = -58.458199688 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-9.166666665' to each side of the equation. 9.166666665 + -9.166666665 + v = -58.458199688 + -9.166666665 Combine like terms: 9.166666665 + -9.166666665 = 0.000000000 0.000000000 + v = -58.458199688 + -9.166666665 v = -58.458199688 + -9.166666665 Combine like terms: -58.458199688 + -9.166666665 = -67.624866353 v = -67.624866353 Simplifying v = -67.624866353Solution
The solution to the problem is based on the solutions from the subproblems. v = {49.291533023, -67.624866353}
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