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Simplifying 59.02 = -0.5126x2 + 12.74x + -1 Reorder the terms: 59.02 = -1 + 12.74x + -0.5126x2 Solving 59.02 = -1 + 12.74x + -0.5126x2 Solving for variable 'x'. Combine like terms: 59.02 + 1 = 60.02 60.02 + -12.74x + 0.5126x2 = -1 + 12.74x + -0.5126x2 + 1 + -12.74x + 0.5126x2 Reorder the terms: 60.02 + -12.74x + 0.5126x2 = -1 + 1 + 12.74x + -12.74x + -0.5126x2 + 0.5126x2 Combine like terms: -1 + 1 = 0 60.02 + -12.74x + 0.5126x2 = 0 + 12.74x + -12.74x + -0.5126x2 + 0.5126x2 60.02 + -12.74x + 0.5126x2 = 12.74x + -12.74x + -0.5126x2 + 0.5126x2 Combine like terms: 12.74x + -12.74x = 0.00 60.02 + -12.74x + 0.5126x2 = 0.00 + -0.5126x2 + 0.5126x2 60.02 + -12.74x + 0.5126x2 = -0.5126x2 + 0.5126x2 Combine like terms: -0.5126x2 + 0.5126x2 = 0.0000 60.02 + -12.74x + 0.5126x2 = 0.0000 Begin completing the square. Divide all terms by 0.5126 the coefficient of the squared term: Divide each side by '0.5126'. 117.0893484 + -24.85368709x + x2 = 0 Move the constant term to the right: Add '-117.0893484' to each side of the equation. 117.0893484 + -24.85368709x + -117.0893484 + x2 = 0 + -117.0893484 Reorder the terms: 117.0893484 + -117.0893484 + -24.85368709x + x2 = 0 + -117.0893484 Combine like terms: 117.0893484 + -117.0893484 = 0.0000000 0.0000000 + -24.85368709x + x2 = 0 + -117.0893484 -24.85368709x + x2 = 0 + -117.0893484 Combine like terms: 0 + -117.0893484 = -117.0893484 -24.85368709x + x2 = -117.0893484 The x term is -24.85368709x. Take half its coefficient (-12.42684355). Square it (154.4264406) and add it to both sides. Add '154.4264406' to each side of the equation. -24.85368709x + 154.4264406 + x2 = -117.0893484 + 154.4264406 Reorder the terms: 154.4264406 + -24.85368709x + x2 = -117.0893484 + 154.4264406 Combine like terms: -117.0893484 + 154.4264406 = 37.3370922 154.4264406 + -24.85368709x + x2 = 37.3370922 Factor a perfect square on the left side: (x + -12.42684355)(x + -12.42684355) = 37.3370922 Calculate the square root of the right side: 6.110408513 Break this problem into two subproblems by setting (x + -12.42684355) equal to 6.110408513 and -6.110408513.Subproblem 1
x + -12.42684355 = 6.110408513 Simplifying x + -12.42684355 = 6.110408513 Reorder the terms: -12.42684355 + x = 6.110408513 Solving -12.42684355 + x = 6.110408513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.42684355' to each side of the equation. -12.42684355 + 12.42684355 + x = 6.110408513 + 12.42684355 Combine like terms: -12.42684355 + 12.42684355 = 0.00000000 0.00000000 + x = 6.110408513 + 12.42684355 x = 6.110408513 + 12.42684355 Combine like terms: 6.110408513 + 12.42684355 = 18.537252063 x = 18.537252063 Simplifying x = 18.537252063Subproblem 2
x + -12.42684355 = -6.110408513 Simplifying x + -12.42684355 = -6.110408513 Reorder the terms: -12.42684355 + x = -6.110408513 Solving -12.42684355 + x = -6.110408513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.42684355' to each side of the equation. -12.42684355 + 12.42684355 + x = -6.110408513 + 12.42684355 Combine like terms: -12.42684355 + 12.42684355 = 0.00000000 0.00000000 + x = -6.110408513 + 12.42684355 x = -6.110408513 + 12.42684355 Combine like terms: -6.110408513 + 12.42684355 = 6.316435037 x = 6.316435037 Simplifying x = 6.316435037Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.537252063, 6.316435037}
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