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Simplifying 71716.9685174653x2 + -72447.34698x + 730.13246476296 = 0 Reorder the terms: 730.13246476296 + -72447.34698x + 71716.9685174653x2 = 0 Solving 730.13246476296 + -72447.34698x + 71716.9685174653x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 71716.9685174653 the coefficient of the squared term: Divide each side by '71716.9685174653'. 0.01018074913 + -1.010184179x + x2 = 0 Move the constant term to the right: Add '-0.01018074913' to each side of the equation. 0.01018074913 + -1.010184179x + -0.01018074913 + x2 = 0 + -0.01018074913 Reorder the terms: 0.01018074913 + -0.01018074913 + -1.010184179x + x2 = 0 + -0.01018074913 Combine like terms: 0.01018074913 + -0.01018074913 = 0.00000000000 0.00000000000 + -1.010184179x + x2 = 0 + -0.01018074913 -1.010184179x + x2 = 0 + -0.01018074913 Combine like terms: 0 + -0.01018074913 = -0.01018074913 -1.010184179x + x2 = -0.01018074913 The x term is -1.010184179x. Take half its coefficient (-0.5050920895). Square it (0.2551180189) and add it to both sides. Add '0.2551180189' to each side of the equation. -1.010184179x + 0.2551180189 + x2 = -0.01018074913 + 0.2551180189 Reorder the terms: 0.2551180189 + -1.010184179x + x2 = -0.01018074913 + 0.2551180189 Combine like terms: -0.01018074913 + 0.2551180189 = 0.24493726977 0.2551180189 + -1.010184179x + x2 = 0.24493726977 Factor a perfect square on the left side: (x + -0.5050920895)(x + -0.5050920895) = 0.24493726977 Calculate the square root of the right side: 0.494911376 Break this problem into two subproblems by setting (x + -0.5050920895) equal to 0.494911376 and -0.494911376.Subproblem 1
x + -0.5050920895 = 0.494911376 Simplifying x + -0.5050920895 = 0.494911376 Reorder the terms: -0.5050920895 + x = 0.494911376 Solving -0.5050920895 + x = 0.494911376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5050920895' to each side of the equation. -0.5050920895 + 0.5050920895 + x = 0.494911376 + 0.5050920895 Combine like terms: -0.5050920895 + 0.5050920895 = 0.0000000000 0.0000000000 + x = 0.494911376 + 0.5050920895 x = 0.494911376 + 0.5050920895 Combine like terms: 0.494911376 + 0.5050920895 = 1.0000034655 x = 1.0000034655 Simplifying x = 1.0000034655Subproblem 2
x + -0.5050920895 = -0.494911376 Simplifying x + -0.5050920895 = -0.494911376 Reorder the terms: -0.5050920895 + x = -0.494911376 Solving -0.5050920895 + x = -0.494911376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5050920895' to each side of the equation. -0.5050920895 + 0.5050920895 + x = -0.494911376 + 0.5050920895 Combine like terms: -0.5050920895 + 0.5050920895 = 0.0000000000 0.0000000000 + x = -0.494911376 + 0.5050920895 x = -0.494911376 + 0.5050920895 Combine like terms: -0.494911376 + 0.5050920895 = 0.0101807135 x = 0.0101807135 Simplifying x = 0.0101807135Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0000034655, 0.0101807135}
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