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Simplifying 400x + 0.1x2 + 17686 = 1100x + -0.01x2 Reorder the terms: 17686 + 400x + 0.1x2 = 1100x + -0.01x2 Solving 17686 + 400x + 0.1x2 = 1100x + -0.01x2 Solving for variable 'x'. Reorder the terms: 17686 + 400x + -1100x + 0.1x2 + 0.01x2 = 1100x + -0.01x2 + -1100x + 0.01x2 Combine like terms: 400x + -1100x = -700x 17686 + -700x + 0.1x2 + 0.01x2 = 1100x + -0.01x2 + -1100x + 0.01x2 Combine like terms: 0.1x2 + 0.01x2 = 0.11x2 17686 + -700x + 0.11x2 = 1100x + -0.01x2 + -1100x + 0.01x2 Reorder the terms: 17686 + -700x + 0.11x2 = 1100x + -1100x + -0.01x2 + 0.01x2 Combine like terms: 1100x + -1100x = 0 17686 + -700x + 0.11x2 = 0 + -0.01x2 + 0.01x2 17686 + -700x + 0.11x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 17686 + -700x + 0.11x2 = 0.00 Begin completing the square. Divide all terms by 0.11 the coefficient of the squared term: Divide each side by '0.11'. 160781.8182 + -6363.636364x + x2 = 0 Move the constant term to the right: Add '-160781.8182' to each side of the equation. 160781.8182 + -6363.636364x + -160781.8182 + x2 = 0 + -160781.8182 Reorder the terms: 160781.8182 + -160781.8182 + -6363.636364x + x2 = 0 + -160781.8182 Combine like terms: 160781.8182 + -160781.8182 = 0.0000 0.0000 + -6363.636364x + x2 = 0 + -160781.8182 -6363.636364x + x2 = 0 + -160781.8182 Combine like terms: 0 + -160781.8182 = -160781.8182 -6363.636364x + x2 = -160781.8182 The x term is -6363.636364x. Take half its coefficient (-3181.818182). Square it (10123966.94) and add it to both sides. Add '10123966.94' to each side of the equation. -6363.636364x + 10123966.94 + x2 = -160781.8182 + 10123966.94 Reorder the terms: 10123966.94 + -6363.636364x + x2 = -160781.8182 + 10123966.94 Combine like terms: -160781.8182 + 10123966.94 = 9963185.1218 10123966.94 + -6363.636364x + x2 = 9963185.1218 Factor a perfect square on the left side: (x + -3181.818182)(x + -3181.818182) = 9963185.1218 Calculate the square root of the right side: 3156.451349506 Break this problem into two subproblems by setting (x + -3181.818182) equal to 3156.451349506 and -3156.451349506.Subproblem 1
x + -3181.818182 = 3156.451349506 Simplifying x + -3181.818182 = 3156.451349506 Reorder the terms: -3181.818182 + x = 3156.451349506 Solving -3181.818182 + x = 3156.451349506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3181.818182' to each side of the equation. -3181.818182 + 3181.818182 + x = 3156.451349506 + 3181.818182 Combine like terms: -3181.818182 + 3181.818182 = 0.000000 0.000000 + x = 3156.451349506 + 3181.818182 x = 3156.451349506 + 3181.818182 Combine like terms: 3156.451349506 + 3181.818182 = 6338.269531506 x = 6338.269531506 Simplifying x = 6338.269531506Subproblem 2
x + -3181.818182 = -3156.451349506 Simplifying x + -3181.818182 = -3156.451349506 Reorder the terms: -3181.818182 + x = -3156.451349506 Solving -3181.818182 + x = -3156.451349506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3181.818182' to each side of the equation. -3181.818182 + 3181.818182 + x = -3156.451349506 + 3181.818182 Combine like terms: -3181.818182 + 3181.818182 = 0.000000 0.000000 + x = -3156.451349506 + 3181.818182 x = -3156.451349506 + 3181.818182 Combine like terms: -3156.451349506 + 3181.818182 = 25.366832494 x = 25.366832494 Simplifying x = 25.366832494Solution
The solution to the problem is based on the solutions from the subproblems. x = {6338.269531506, 25.366832494}
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