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Simplifying 56 = -0.00211x2 + 1.06x Reorder the terms: 56 = 1.06x + -0.00211x2 Solving 56 = 1.06x + -0.00211x2 Solving for variable 'x'. Reorder the terms: 56 + -1.06x + 0.00211x2 = 1.06x + -1.06x + -0.00211x2 + 0.00211x2 Combine like terms: 1.06x + -1.06x = 0.00 56 + -1.06x + 0.00211x2 = 0.00 + -0.00211x2 + 0.00211x2 56 + -1.06x + 0.00211x2 = -0.00211x2 + 0.00211x2 Combine like terms: -0.00211x2 + 0.00211x2 = 0.00000 56 + -1.06x + 0.00211x2 = 0.00000 Begin completing the square. Divide all terms by 0.00211 the coefficient of the squared term: Divide each side by '0.00211'. 26540.28436 + -502.3696682x + x2 = 0 Move the constant term to the right: Add '-26540.28436' to each side of the equation. 26540.28436 + -502.3696682x + -26540.28436 + x2 = 0 + -26540.28436 Reorder the terms: 26540.28436 + -26540.28436 + -502.3696682x + x2 = 0 + -26540.28436 Combine like terms: 26540.28436 + -26540.28436 = 0.00000 0.00000 + -502.3696682x + x2 = 0 + -26540.28436 -502.3696682x + x2 = 0 + -26540.28436 Combine like terms: 0 + -26540.28436 = -26540.28436 -502.3696682x + x2 = -26540.28436 The x term is -502.3696682x. Take half its coefficient (-251.1848341). Square it (63093.82088) and add it to both sides. Add '63093.82088' to each side of the equation. -502.3696682x + 63093.82088 + x2 = -26540.28436 + 63093.82088 Reorder the terms: 63093.82088 + -502.3696682x + x2 = -26540.28436 + 63093.82088 Combine like terms: -26540.28436 + 63093.82088 = 36553.53652 63093.82088 + -502.3696682x + x2 = 36553.53652 Factor a perfect square on the left side: (x + -251.1848341)(x + -251.1848341) = 36553.53652 Calculate the square root of the right side: 191.189791882 Break this problem into two subproblems by setting (x + -251.1848341) equal to 191.189791882 and -191.189791882.Subproblem 1
x + -251.1848341 = 191.189791882 Simplifying x + -251.1848341 = 191.189791882 Reorder the terms: -251.1848341 + x = 191.189791882 Solving -251.1848341 + x = 191.189791882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '251.1848341' to each side of the equation. -251.1848341 + 251.1848341 + x = 191.189791882 + 251.1848341 Combine like terms: -251.1848341 + 251.1848341 = 0.0000000 0.0000000 + x = 191.189791882 + 251.1848341 x = 191.189791882 + 251.1848341 Combine like terms: 191.189791882 + 251.1848341 = 442.374625982 x = 442.374625982 Simplifying x = 442.374625982Subproblem 2
x + -251.1848341 = -191.189791882 Simplifying x + -251.1848341 = -191.189791882 Reorder the terms: -251.1848341 + x = -191.189791882 Solving -251.1848341 + x = -191.189791882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '251.1848341' to each side of the equation. -251.1848341 + 251.1848341 + x = -191.189791882 + 251.1848341 Combine like terms: -251.1848341 + 251.1848341 = 0.0000000 0.0000000 + x = -191.189791882 + 251.1848341 x = -191.189791882 + 251.1848341 Combine like terms: -191.189791882 + 251.1848341 = 59.995042218 x = 59.995042218 Simplifying x = 59.995042218Solution
The solution to the problem is based on the solutions from the subproblems. x = {442.374625982, 59.995042218}
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