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Simplifying 498.73x2 + 249.4x + 0.0721 = 0 Reorder the terms: 0.0721 + 249.4x + 498.73x2 = 0 Solving 0.0721 + 249.4x + 498.73x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 498.73 the coefficient of the squared term: Divide each side by '498.73'. 0.0001445672007 + 0.5000701783x + x2 = 0 Move the constant term to the right: Add '-0.0001445672007' to each side of the equation. 0.0001445672007 + 0.5000701783x + -0.0001445672007 + x2 = 0 + -0.0001445672007 Reorder the terms: 0.0001445672007 + -0.0001445672007 + 0.5000701783x + x2 = 0 + -0.0001445672007 Combine like terms: 0.0001445672007 + -0.0001445672007 = 0.0000000000000 0.0000000000000 + 0.5000701783x + x2 = 0 + -0.0001445672007 0.5000701783x + x2 = 0 + -0.0001445672007 Combine like terms: 0 + -0.0001445672007 = -0.0001445672007 0.5000701783x + x2 = -0.0001445672007 The x term is 0.5000701783x. Take half its coefficient (0.2500350892). Square it (0.06251754583) and add it to both sides. Add '0.06251754583' to each side of the equation. 0.5000701783x + 0.06251754583 + x2 = -0.0001445672007 + 0.06251754583 Reorder the terms: 0.06251754583 + 0.5000701783x + x2 = -0.0001445672007 + 0.06251754583 Combine like terms: -0.0001445672007 + 0.06251754583 = 0.0623729786293 0.06251754583 + 0.5000701783x + x2 = 0.0623729786293 Factor a perfect square on the left side: (x + 0.2500350892)(x + 0.2500350892) = 0.0623729786293 Calculate the square root of the right side: 0.249745828 Break this problem into two subproblems by setting (x + 0.2500350892) equal to 0.249745828 and -0.249745828.Subproblem 1
x + 0.2500350892 = 0.249745828 Simplifying x + 0.2500350892 = 0.249745828 Reorder the terms: 0.2500350892 + x = 0.249745828 Solving 0.2500350892 + x = 0.249745828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2500350892' to each side of the equation. 0.2500350892 + -0.2500350892 + x = 0.249745828 + -0.2500350892 Combine like terms: 0.2500350892 + -0.2500350892 = 0.0000000000 0.0000000000 + x = 0.249745828 + -0.2500350892 x = 0.249745828 + -0.2500350892 Combine like terms: 0.249745828 + -0.2500350892 = -0.0002892612 x = -0.0002892612 Simplifying x = -0.0002892612Subproblem 2
x + 0.2500350892 = -0.249745828 Simplifying x + 0.2500350892 = -0.249745828 Reorder the terms: 0.2500350892 + x = -0.249745828 Solving 0.2500350892 + x = -0.249745828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2500350892' to each side of the equation. 0.2500350892 + -0.2500350892 + x = -0.249745828 + -0.2500350892 Combine like terms: 0.2500350892 + -0.2500350892 = 0.0000000000 0.0000000000 + x = -0.249745828 + -0.2500350892 x = -0.249745828 + -0.2500350892 Combine like terms: -0.249745828 + -0.2500350892 = -0.4997809172 x = -0.4997809172 Simplifying x = -0.4997809172Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0002892612, -0.4997809172}
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