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Simplifying X2 + -68X + 46 = 0 Reorder the terms: 46 + -68X + X2 = 0 Solving 46 + -68X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-46' to each side of the equation. 46 + -68X + -46 + X2 = 0 + -46 Reorder the terms: 46 + -46 + -68X + X2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + -68X + X2 = 0 + -46 -68X + X2 = 0 + -46 Combine like terms: 0 + -46 = -46 -68X + X2 = -46 The X term is -68X. Take half its coefficient (-34). Square it (1156) and add it to both sides. Add '1156' to each side of the equation. -68X + 1156 + X2 = -46 + 1156 Reorder the terms: 1156 + -68X + X2 = -46 + 1156 Combine like terms: -46 + 1156 = 1110 1156 + -68X + X2 = 1110 Factor a perfect square on the left side: (X + -34)(X + -34) = 1110 Calculate the square root of the right side: 33.316662498 Break this problem into two subproblems by setting (X + -34) equal to 33.316662498 and -33.316662498.Subproblem 1
X + -34 = 33.316662498 Simplifying X + -34 = 33.316662498 Reorder the terms: -34 + X = 33.316662498 Solving -34 + X = 33.316662498 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '34' to each side of the equation. -34 + 34 + X = 33.316662498 + 34 Combine like terms: -34 + 34 = 0 0 + X = 33.316662498 + 34 X = 33.316662498 + 34 Combine like terms: 33.316662498 + 34 = 67.316662498 X = 67.316662498 Simplifying X = 67.316662498Subproblem 2
X + -34 = -33.316662498 Simplifying X + -34 = -33.316662498 Reorder the terms: -34 + X = -33.316662498 Solving -34 + X = -33.316662498 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '34' to each side of the equation. -34 + 34 + X = -33.316662498 + 34 Combine like terms: -34 + 34 = 0 0 + X = -33.316662498 + 34 X = -33.316662498 + 34 Combine like terms: -33.316662498 + 34 = 0.683337502 X = 0.683337502 Simplifying X = 0.683337502Solution
The solution to the problem is based on the solutions from the subproblems. X = {67.316662498, 0.683337502}
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