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Simplifying 1000x2 + 71x + -71 = 0 Reorder the terms: -71 + 71x + 1000x2 = 0 Solving -71 + 71x + 1000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1000 the coefficient of the squared term: Divide each side by '1000'. -0.071 + 0.071x + x2 = 0 Move the constant term to the right: Add '0.071' to each side of the equation. -0.071 + 0.071x + 0.071 + x2 = 0 + 0.071 Reorder the terms: -0.071 + 0.071 + 0.071x + x2 = 0 + 0.071 Combine like terms: -0.071 + 0.071 = 0.000 0.000 + 0.071x + x2 = 0 + 0.071 0.071x + x2 = 0 + 0.071 Combine like terms: 0 + 0.071 = 0.071 0.071x + x2 = 0.071 The x term is 0.071x. Take half its coefficient (0.0355). Square it (0.00126025) and add it to both sides. Add '0.00126025' to each side of the equation. 0.071x + 0.00126025 + x2 = 0.071 + 0.00126025 Reorder the terms: 0.00126025 + 0.071x + x2 = 0.071 + 0.00126025 Combine like terms: 0.071 + 0.00126025 = 0.07226025 0.00126025 + 0.071x + x2 = 0.07226025 Factor a perfect square on the left side: (x + 0.0355)(x + 0.0355) = 0.07226025 Calculate the square root of the right side: 0.268812667 Break this problem into two subproblems by setting (x + 0.0355) equal to 0.268812667 and -0.268812667.Subproblem 1
x + 0.0355 = 0.268812667 Simplifying x + 0.0355 = 0.268812667 Reorder the terms: 0.0355 + x = 0.268812667 Solving 0.0355 + x = 0.268812667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0355' to each side of the equation. 0.0355 + -0.0355 + x = 0.268812667 + -0.0355 Combine like terms: 0.0355 + -0.0355 = 0.0000 0.0000 + x = 0.268812667 + -0.0355 x = 0.268812667 + -0.0355 Combine like terms: 0.268812667 + -0.0355 = 0.233312667 x = 0.233312667 Simplifying x = 0.233312667Subproblem 2
x + 0.0355 = -0.268812667 Simplifying x + 0.0355 = -0.268812667 Reorder the terms: 0.0355 + x = -0.268812667 Solving 0.0355 + x = -0.268812667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0355' to each side of the equation. 0.0355 + -0.0355 + x = -0.268812667 + -0.0355 Combine like terms: 0.0355 + -0.0355 = 0.0000 0.0000 + x = -0.268812667 + -0.0355 x = -0.268812667 + -0.0355 Combine like terms: -0.268812667 + -0.0355 = -0.304312667 x = -0.304312667 Simplifying x = -0.304312667Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.233312667, -0.304312667}
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