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Simplifying -0.001x2 + 3x + -525 + 0.55x = 0 Reorder the terms: -525 + 3x + 0.55x + -0.001x2 = 0 Combine like terms: 3x + 0.55x = 3.55x -525 + 3.55x + -0.001x2 = 0 Solving -525 + 3.55x + -0.001x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.001 the coefficient of the squared term: Divide each side by '-0.001'. 525000 + -3550x + x2 = 0 Move the constant term to the right: Add '-525000' to each side of the equation. 525000 + -3550x + -525000 + x2 = 0 + -525000 Reorder the terms: 525000 + -525000 + -3550x + x2 = 0 + -525000 Combine like terms: 525000 + -525000 = 0 0 + -3550x + x2 = 0 + -525000 -3550x + x2 = 0 + -525000 Combine like terms: 0 + -525000 = -525000 -3550x + x2 = -525000 The x term is -3550x. Take half its coefficient (-1775). Square it (3150625) and add it to both sides. Add '3150625' to each side of the equation. -3550x + 3150625 + x2 = -525000 + 3150625 Reorder the terms: 3150625 + -3550x + x2 = -525000 + 3150625 Combine like terms: -525000 + 3150625 = 2625625 3150625 + -3550x + x2 = 2625625 Factor a perfect square on the left side: (x + -1775)(x + -1775) = 2625625 Calculate the square root of the right side: 1620.37804231 Break this problem into two subproblems by setting (x + -1775) equal to 1620.37804231 and -1620.37804231.Subproblem 1
x + -1775 = 1620.37804231 Simplifying x + -1775 = 1620.37804231 Reorder the terms: -1775 + x = 1620.37804231 Solving -1775 + x = 1620.37804231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1775' to each side of the equation. -1775 + 1775 + x = 1620.37804231 + 1775 Combine like terms: -1775 + 1775 = 0 0 + x = 1620.37804231 + 1775 x = 1620.37804231 + 1775 Combine like terms: 1620.37804231 + 1775 = 3395.37804231 x = 3395.37804231 Simplifying x = 3395.37804231Subproblem 2
x + -1775 = -1620.37804231 Simplifying x + -1775 = -1620.37804231 Reorder the terms: -1775 + x = -1620.37804231 Solving -1775 + x = -1620.37804231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1775' to each side of the equation. -1775 + 1775 + x = -1620.37804231 + 1775 Combine like terms: -1775 + 1775 = 0 0 + x = -1620.37804231 + 1775 x = -1620.37804231 + 1775 Combine like terms: -1620.37804231 + 1775 = 154.62195769 x = 154.62195769 Simplifying x = 154.62195769Solution
The solution to the problem is based on the solutions from the subproblems. x = {3395.37804231, 154.62195769}
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