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Simplifying x2 + -29.64102564x + 118.5641026 = 0 Reorder the terms: 118.5641026 + -29.64102564x + x2 = 0 Solving 118.5641026 + -29.64102564x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-118.5641026' to each side of the equation. 118.5641026 + -29.64102564x + -118.5641026 + x2 = 0 + -118.5641026 Reorder the terms: 118.5641026 + -118.5641026 + -29.64102564x + x2 = 0 + -118.5641026 Combine like terms: 118.5641026 + -118.5641026 = 0.0000000 0.0000000 + -29.64102564x + x2 = 0 + -118.5641026 -29.64102564x + x2 = 0 + -118.5641026 Combine like terms: 0 + -118.5641026 = -118.5641026 -29.64102564x + x2 = -118.5641026 The x term is -29.64102564x. Take half its coefficient (-14.82051282). Square it (219.6476002) and add it to both sides. Add '219.6476002' to each side of the equation. -29.64102564x + 219.6476002 + x2 = -118.5641026 + 219.6476002 Reorder the terms: 219.6476002 + -29.64102564x + x2 = -118.5641026 + 219.6476002 Combine like terms: -118.5641026 + 219.6476002 = 101.0834976 219.6476002 + -29.64102564x + x2 = 101.0834976 Factor a perfect square on the left side: (x + -14.82051282)(x + -14.82051282) = 101.0834976 Calculate the square root of the right side: 10.054028924 Break this problem into two subproblems by setting (x + -14.82051282) equal to 10.054028924 and -10.054028924.Subproblem 1
x + -14.82051282 = 10.054028924 Simplifying x + -14.82051282 = 10.054028924 Reorder the terms: -14.82051282 + x = 10.054028924 Solving -14.82051282 + x = 10.054028924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.82051282' to each side of the equation. -14.82051282 + 14.82051282 + x = 10.054028924 + 14.82051282 Combine like terms: -14.82051282 + 14.82051282 = 0.00000000 0.00000000 + x = 10.054028924 + 14.82051282 x = 10.054028924 + 14.82051282 Combine like terms: 10.054028924 + 14.82051282 = 24.874541744 x = 24.874541744 Simplifying x = 24.874541744Subproblem 2
x + -14.82051282 = -10.054028924 Simplifying x + -14.82051282 = -10.054028924 Reorder the terms: -14.82051282 + x = -10.054028924 Solving -14.82051282 + x = -10.054028924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.82051282' to each side of the equation. -14.82051282 + 14.82051282 + x = -10.054028924 + 14.82051282 Combine like terms: -14.82051282 + 14.82051282 = 0.00000000 0.00000000 + x = -10.054028924 + 14.82051282 x = -10.054028924 + 14.82051282 Combine like terms: -10.054028924 + 14.82051282 = 4.766483896 x = 4.766483896 Simplifying x = 4.766483896Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.874541744, 4.766483896}
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