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Simplifying 8200(x) = x2 + -11x + 40 Reorder the terms: 8200x = 40 + -11x + x2 Solving 8200x = 40 + -11x + x2 Solving for variable 'x'. Reorder the terms: -40 + 8200x + 11x + -1x2 = 40 + -11x + x2 + -40 + 11x + -1x2 Combine like terms: 8200x + 11x = 8211x -40 + 8211x + -1x2 = 40 + -11x + x2 + -40 + 11x + -1x2 Reorder the terms: -40 + 8211x + -1x2 = 40 + -40 + -11x + 11x + x2 + -1x2 Combine like terms: 40 + -40 = 0 -40 + 8211x + -1x2 = 0 + -11x + 11x + x2 + -1x2 -40 + 8211x + -1x2 = -11x + 11x + x2 + -1x2 Combine like terms: -11x + 11x = 0 -40 + 8211x + -1x2 = 0 + x2 + -1x2 -40 + 8211x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -40 + 8211x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 40 + -8211x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -8211x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -8211x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -8211x + x2 = 0 + -40 -8211x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -8211x + x2 = -40 The x term is -8211x. Take half its coefficient (-4105.5). Square it (16855130.25) and add it to both sides. Add '16855130.25' to each side of the equation. -8211x + 16855130.25 + x2 = -40 + 16855130.25 Reorder the terms: 16855130.25 + -8211x + x2 = -40 + 16855130.25 Combine like terms: -40 + 16855130.25 = 16855090.25 16855130.25 + -8211x + x2 = 16855090.25 Factor a perfect square on the left side: (x + -4105.5)(x + -4105.5) = 16855090.25 Calculate the square root of the right side: 4105.495128483 Break this problem into two subproblems by setting (x + -4105.5) equal to 4105.495128483 and -4105.495128483.Subproblem 1
x + -4105.5 = 4105.495128483 Simplifying x + -4105.5 = 4105.495128483 Reorder the terms: -4105.5 + x = 4105.495128483 Solving -4105.5 + x = 4105.495128483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4105.5' to each side of the equation. -4105.5 + 4105.5 + x = 4105.495128483 + 4105.5 Combine like terms: -4105.5 + 4105.5 = 0.0 0.0 + x = 4105.495128483 + 4105.5 x = 4105.495128483 + 4105.5 Combine like terms: 4105.495128483 + 4105.5 = 8210.995128483 x = 8210.995128483 Simplifying x = 8210.995128483Subproblem 2
x + -4105.5 = -4105.495128483 Simplifying x + -4105.5 = -4105.495128483 Reorder the terms: -4105.5 + x = -4105.495128483 Solving -4105.5 + x = -4105.495128483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4105.5' to each side of the equation. -4105.5 + 4105.5 + x = -4105.495128483 + 4105.5 Combine like terms: -4105.5 + 4105.5 = 0.0 0.0 + x = -4105.495128483 + 4105.5 x = -4105.495128483 + 4105.5 Combine like terms: -4105.495128483 + 4105.5 = 0.004871517 x = 0.004871517 Simplifying x = 0.004871517Solution
The solution to the problem is based on the solutions from the subproblems. x = {8210.995128483, 0.004871517}
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