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Simplifying 200 = 1.1x + 0.06x2 Solving 200 = 1.1x + 0.06x2 Solving for variable 'x'. Reorder the terms: 200 + -1.1x + -0.06x2 = 1.1x + -1.1x + 0.06x2 + -0.06x2 Combine like terms: 1.1x + -1.1x = 0.0 200 + -1.1x + -0.06x2 = 0.0 + 0.06x2 + -0.06x2 200 + -1.1x + -0.06x2 = 0.06x2 + -0.06x2 Combine like terms: 0.06x2 + -0.06x2 = 0.00 200 + -1.1x + -0.06x2 = 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 + 18.33333333x + x2 = 0 Move the constant term to the right: Add '3333.333333' to each side of the equation. -3333.333333 + 18.33333333x + 3333.333333 + x2 = 0 + 3333.333333 Reorder the terms: -3333.333333 + 3333.333333 + 18.33333333x + x2 = 0 + 3333.333333 Combine like terms: -3333.333333 + 3333.333333 = 0.000000 0.000000 + 18.33333333x + x2 = 0 + 3333.333333 18.33333333x + x2 = 0 + 3333.333333 Combine like terms: 0 + 3333.333333 = 3333.333333 18.33333333x + x2 = 3333.333333 The x term is 18.33333333x. 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. 18.33333333x + 84.02777775 + x2 = 3333.333333 + 84.02777775 Reorder the terms: 84.02777775 + 18.33333333x + x2 = 3333.333333 + 84.02777775 Combine like terms: 3333.333333 + 84.02777775 = 3417.36111075 84.02777775 + 18.33333333x + x2 = 3417.36111075 Factor a perfect square on the left side: (x + 9.166666665)(x + 9.166666665) = 3417.36111075 Calculate the square root of the right side: 58.458199688 Break this problem into two subproblems by setting (x + 9.166666665) equal to 58.458199688 and -58.458199688.Subproblem 1
x + 9.166666665 = 58.458199688 Simplifying x + 9.166666665 = 58.458199688 Reorder the terms: 9.166666665 + x = 58.458199688 Solving 9.166666665 + x = 58.458199688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.166666665' to each side of the equation. 9.166666665 + -9.166666665 + x = 58.458199688 + -9.166666665 Combine like terms: 9.166666665 + -9.166666665 = 0.000000000 0.000000000 + x = 58.458199688 + -9.166666665 x = 58.458199688 + -9.166666665 Combine like terms: 58.458199688 + -9.166666665 = 49.291533023 x = 49.291533023 Simplifying x = 49.291533023Subproblem 2
x + 9.166666665 = -58.458199688 Simplifying x + 9.166666665 = -58.458199688 Reorder the terms: 9.166666665 + x = -58.458199688 Solving 9.166666665 + x = -58.458199688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.166666665' to each side of the equation. 9.166666665 + -9.166666665 + x = -58.458199688 + -9.166666665 Combine like terms: 9.166666665 + -9.166666665 = 0.000000000 0.000000000 + x = -58.458199688 + -9.166666665 x = -58.458199688 + -9.166666665 Combine like terms: -58.458199688 + -9.166666665 = -67.624866353 x = -67.624866353 Simplifying x = -67.624866353Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.291533023, -67.624866353}
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