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Simplifying 542.0312136x2 + -549.1529362x + 6.875722603 = 0 Reorder the terms: 6.875722603 + -549.1529362x + 542.0312136x2 = 0 Solving 6.875722603 + -549.1529362x + 542.0312136x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 542.0312136 the coefficient of the squared term: Divide each side by '542.0312136'. 0.01268510453 + -1.013138953x + x2 = 0 Move the constant term to the right: Add '-0.01268510453' to each side of the equation. 0.01268510453 + -1.013138953x + -0.01268510453 + x2 = 0 + -0.01268510453 Reorder the terms: 0.01268510453 + -0.01268510453 + -1.013138953x + x2 = 0 + -0.01268510453 Combine like terms: 0.01268510453 + -0.01268510453 = 0.00000000000 0.00000000000 + -1.013138953x + x2 = 0 + -0.01268510453 -1.013138953x + x2 = 0 + -0.01268510453 Combine like terms: 0 + -0.01268510453 = -0.01268510453 -1.013138953x + x2 = -0.01268510453 The x term is -1.013138953x. Take half its coefficient (-0.5065694765). Square it (0.2566126345) and add it to both sides. Add '0.2566126345' to each side of the equation. -1.013138953x + 0.2566126345 + x2 = -0.01268510453 + 0.2566126345 Reorder the terms: 0.2566126345 + -1.013138953x + x2 = -0.01268510453 + 0.2566126345 Combine like terms: -0.01268510453 + 0.2566126345 = 0.24392752997 0.2566126345 + -1.013138953x + x2 = 0.24392752997 Factor a perfect square on the left side: (x + -0.5065694765)(x + -0.5065694765) = 0.24392752997 Calculate the square root of the right side: 0.4938902 Break this problem into two subproblems by setting (x + -0.5065694765) equal to 0.4938902 and -0.4938902.Subproblem 1
x + -0.5065694765 = 0.4938902 Simplifying x + -0.5065694765 = 0.4938902 Reorder the terms: -0.5065694765 + x = 0.4938902 Solving -0.5065694765 + x = 0.4938902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5065694765' to each side of the equation. -0.5065694765 + 0.5065694765 + x = 0.4938902 + 0.5065694765 Combine like terms: -0.5065694765 + 0.5065694765 = 0.0000000000 0.0000000000 + x = 0.4938902 + 0.5065694765 x = 0.4938902 + 0.5065694765 Combine like terms: 0.4938902 + 0.5065694765 = 1.0004596765 x = 1.0004596765 Simplifying x = 1.0004596765Subproblem 2
x + -0.5065694765 = -0.4938902 Simplifying x + -0.5065694765 = -0.4938902 Reorder the terms: -0.5065694765 + x = -0.4938902 Solving -0.5065694765 + x = -0.4938902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5065694765' to each side of the equation. -0.5065694765 + 0.5065694765 + x = -0.4938902 + 0.5065694765 Combine like terms: -0.5065694765 + 0.5065694765 = 0.0000000000 0.0000000000 + x = -0.4938902 + 0.5065694765 x = -0.4938902 + 0.5065694765 Combine like terms: -0.4938902 + 0.5065694765 = 0.0126792765 x = 0.0126792765 Simplifying x = 0.0126792765Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0004596765, 0.0126792765}
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