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Simplifying -9.53x2 + 5250.985x + -382190.335 = 0 Reorder the terms: -382190.335 + 5250.985x + -9.53x2 = 0 Solving -382190.335 + 5250.985x + -9.53x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9.53 the coefficient of the squared term: Divide each side by '-9.53'. 40103.91763 + -550.9952781x + x2 = 0 Move the constant term to the right: Add '-40103.91763' to each side of the equation. 40103.91763 + -550.9952781x + -40103.91763 + x2 = 0 + -40103.91763 Reorder the terms: 40103.91763 + -40103.91763 + -550.9952781x + x2 = 0 + -40103.91763 Combine like terms: 40103.91763 + -40103.91763 = 0.00000 0.00000 + -550.9952781x + x2 = 0 + -40103.91763 -550.9952781x + x2 = 0 + -40103.91763 Combine like terms: 0 + -40103.91763 = -40103.91763 -550.9952781x + x2 = -40103.91763 The x term is -550.9952781x. Take half its coefficient (-275.4976391). Square it (75898.94915) and add it to both sides. Add '75898.94915' to each side of the equation. -550.9952781x + 75898.94915 + x2 = -40103.91763 + 75898.94915 Reorder the terms: 75898.94915 + -550.9952781x + x2 = -40103.91763 + 75898.94915 Combine like terms: -40103.91763 + 75898.94915 = 35795.03152 75898.94915 + -550.9952781x + x2 = 35795.03152 Factor a perfect square on the left side: (x + -275.4976391)(x + -275.4976391) = 35795.03152 Calculate the square root of the right side: 189.195749212 Break this problem into two subproblems by setting (x + -275.4976391) equal to 189.195749212 and -189.195749212.Subproblem 1
x + -275.4976391 = 189.195749212 Simplifying x + -275.4976391 = 189.195749212 Reorder the terms: -275.4976391 + x = 189.195749212 Solving -275.4976391 + x = 189.195749212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '275.4976391' to each side of the equation. -275.4976391 + 275.4976391 + x = 189.195749212 + 275.4976391 Combine like terms: -275.4976391 + 275.4976391 = 0.0000000 0.0000000 + x = 189.195749212 + 275.4976391 x = 189.195749212 + 275.4976391 Combine like terms: 189.195749212 + 275.4976391 = 464.693388312 x = 464.693388312 Simplifying x = 464.693388312Subproblem 2
x + -275.4976391 = -189.195749212 Simplifying x + -275.4976391 = -189.195749212 Reorder the terms: -275.4976391 + x = -189.195749212 Solving -275.4976391 + x = -189.195749212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '275.4976391' to each side of the equation. -275.4976391 + 275.4976391 + x = -189.195749212 + 275.4976391 Combine like terms: -275.4976391 + 275.4976391 = 0.0000000 0.0000000 + x = -189.195749212 + 275.4976391 x = -189.195749212 + 275.4976391 Combine like terms: -189.195749212 + 275.4976391 = 86.301889888 x = 86.301889888 Simplifying x = 86.301889888Solution
The solution to the problem is based on the solutions from the subproblems. x = {464.693388312, 86.301889888}
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