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Simplifying 41x2 + -80x + -3500 = 0 Reorder the terms: -3500 + -80x + 41x2 = 0 Solving -3500 + -80x + 41x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 41 the coefficient of the squared term: Divide each side by '41'. -85.36585366 + -1.951219512x + x2 = 0 Move the constant term to the right: Add '85.36585366' to each side of the equation. -85.36585366 + -1.951219512x + 85.36585366 + x2 = 0 + 85.36585366 Reorder the terms: -85.36585366 + 85.36585366 + -1.951219512x + x2 = 0 + 85.36585366 Combine like terms: -85.36585366 + 85.36585366 = 0.00000000 0.00000000 + -1.951219512x + x2 = 0 + 85.36585366 -1.951219512x + x2 = 0 + 85.36585366 Combine like terms: 0 + 85.36585366 = 85.36585366 -1.951219512x + x2 = 85.36585366 The x term is -1.951219512x. Take half its coefficient (-0.975609756). Square it (0.9518143960) and add it to both sides. Add '0.9518143960' to each side of the equation. -1.951219512x + 0.9518143960 + x2 = 85.36585366 + 0.9518143960 Reorder the terms: 0.9518143960 + -1.951219512x + x2 = 85.36585366 + 0.9518143960 Combine like terms: 85.36585366 + 0.9518143960 = 86.317668056 0.9518143960 + -1.951219512x + x2 = 86.317668056 Factor a perfect square on the left side: (x + -0.975609756)(x + -0.975609756) = 86.317668056 Calculate the square root of the right side: 9.290730222 Break this problem into two subproblems by setting (x + -0.975609756) equal to 9.290730222 and -9.290730222.Subproblem 1
x + -0.975609756 = 9.290730222 Simplifying x + -0.975609756 = 9.290730222 Reorder the terms: -0.975609756 + x = 9.290730222 Solving -0.975609756 + x = 9.290730222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.975609756' to each side of the equation. -0.975609756 + 0.975609756 + x = 9.290730222 + 0.975609756 Combine like terms: -0.975609756 + 0.975609756 = 0.000000000 0.000000000 + x = 9.290730222 + 0.975609756 x = 9.290730222 + 0.975609756 Combine like terms: 9.290730222 + 0.975609756 = 10.266339978 x = 10.266339978 Simplifying x = 10.266339978Subproblem 2
x + -0.975609756 = -9.290730222 Simplifying x + -0.975609756 = -9.290730222 Reorder the terms: -0.975609756 + x = -9.290730222 Solving -0.975609756 + x = -9.290730222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.975609756' to each side of the equation. -0.975609756 + 0.975609756 + x = -9.290730222 + 0.975609756 Combine like terms: -0.975609756 + 0.975609756 = 0.000000000 0.000000000 + x = -9.290730222 + 0.975609756 x = -9.290730222 + 0.975609756 Combine like terms: -9.290730222 + 0.975609756 = -8.315120466 x = -8.315120466 Simplifying x = -8.315120466Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.266339978, -8.315120466}
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