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Simplifying 0 = -0.0241x2 + x + 5.5 Reorder the terms: 0 = 5.5 + x + -0.0241x2 Solving 0 = 5.5 + x + -0.0241x2 Solving for variable 'x'. Combine like terms: 0 + -5.5 = -5.5 -5.5 + -1x + 0.0241x2 = 5.5 + x + -0.0241x2 + -5.5 + -1x + 0.0241x2 Reorder the terms: -5.5 + -1x + 0.0241x2 = 5.5 + -5.5 + x + -1x + -0.0241x2 + 0.0241x2 Combine like terms: 5.5 + -5.5 = 0.0 -5.5 + -1x + 0.0241x2 = 0.0 + x + -1x + -0.0241x2 + 0.0241x2 -5.5 + -1x + 0.0241x2 = x + -1x + -0.0241x2 + 0.0241x2 Combine like terms: x + -1x = 0 -5.5 + -1x + 0.0241x2 = 0 + -0.0241x2 + 0.0241x2 -5.5 + -1x + 0.0241x2 = -0.0241x2 + 0.0241x2 Combine like terms: -0.0241x2 + 0.0241x2 = 0.0000 -5.5 + -1x + 0.0241x2 = 0.0000 Begin completing the square. Divide all terms by 0.0241 the coefficient of the squared term: Divide each side by '0.0241'. -228.2157676 + -41.49377593x + x2 = 0 Move the constant term to the right: Add '228.2157676' to each side of the equation. -228.2157676 + -41.49377593x + 228.2157676 + x2 = 0 + 228.2157676 Reorder the terms: -228.2157676 + 228.2157676 + -41.49377593x + x2 = 0 + 228.2157676 Combine like terms: -228.2157676 + 228.2157676 = 0.0000000 0.0000000 + -41.49377593x + x2 = 0 + 228.2157676 -41.49377593x + x2 = 0 + 228.2157676 Combine like terms: 0 + 228.2157676 = 228.2157676 -41.49377593x + x2 = 228.2157676 The x term is -41.49377593x. Take half its coefficient (-20.74688797). Square it (430.4333604) and add it to both sides. Add '430.4333604' to each side of the equation. -41.49377593x + 430.4333604 + x2 = 228.2157676 + 430.4333604 Reorder the terms: 430.4333604 + -41.49377593x + x2 = 228.2157676 + 430.4333604 Combine like terms: 228.2157676 + 430.4333604 = 658.649128 430.4333604 + -41.49377593x + x2 = 658.649128 Factor a perfect square on the left side: (x + -20.74688797)(x + -20.74688797) = 658.649128 Calculate the square root of the right side: 25.66416038 Break this problem into two subproblems by setting (x + -20.74688797) equal to 25.66416038 and -25.66416038.Subproblem 1
x + -20.74688797 = 25.66416038 Simplifying x + -20.74688797 = 25.66416038 Reorder the terms: -20.74688797 + x = 25.66416038 Solving -20.74688797 + x = 25.66416038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.74688797' to each side of the equation. -20.74688797 + 20.74688797 + x = 25.66416038 + 20.74688797 Combine like terms: -20.74688797 + 20.74688797 = 0.00000000 0.00000000 + x = 25.66416038 + 20.74688797 x = 25.66416038 + 20.74688797 Combine like terms: 25.66416038 + 20.74688797 = 46.41104835 x = 46.41104835 Simplifying x = 46.41104835Subproblem 2
x + -20.74688797 = -25.66416038 Simplifying x + -20.74688797 = -25.66416038 Reorder the terms: -20.74688797 + x = -25.66416038 Solving -20.74688797 + x = -25.66416038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.74688797' to each side of the equation. -20.74688797 + 20.74688797 + x = -25.66416038 + 20.74688797 Combine like terms: -20.74688797 + 20.74688797 = 0.00000000 0.00000000 + x = -25.66416038 + 20.74688797 x = -25.66416038 + 20.74688797 Combine like terms: -25.66416038 + 20.74688797 = -4.91727241 x = -4.91727241 Simplifying x = -4.91727241Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.41104835, -4.91727241}
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