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Simplifying x2 + -4x + -1996 = 0 Reorder the terms: -1996 + -4x + x2 = 0 Solving -1996 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1996' to each side of the equation. -1996 + -4x + 1996 + x2 = 0 + 1996 Reorder the terms: -1996 + 1996 + -4x + x2 = 0 + 1996 Combine like terms: -1996 + 1996 = 0 0 + -4x + x2 = 0 + 1996 -4x + x2 = 0 + 1996 Combine like terms: 0 + 1996 = 1996 -4x + x2 = 1996 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 1996 + 4 Reorder the terms: 4 + -4x + x2 = 1996 + 4 Combine like terms: 1996 + 4 = 2000 4 + -4x + x2 = 2000 Factor a perfect square on the left side: (x + -2)(x + -2) = 2000 Calculate the square root of the right side: 44.72135955 Break this problem into two subproblems by setting (x + -2) equal to 44.72135955 and -44.72135955.Subproblem 1
x + -2 = 44.72135955 Simplifying x + -2 = 44.72135955 Reorder the terms: -2 + x = 44.72135955 Solving -2 + x = 44.72135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 44.72135955 + 2 Combine like terms: -2 + 2 = 0 0 + x = 44.72135955 + 2 x = 44.72135955 + 2 Combine like terms: 44.72135955 + 2 = 46.72135955 x = 46.72135955 Simplifying x = 46.72135955Subproblem 2
x + -2 = -44.72135955 Simplifying x + -2 = -44.72135955 Reorder the terms: -2 + x = -44.72135955 Solving -2 + x = -44.72135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -44.72135955 + 2 Combine like terms: -2 + 2 = 0 0 + x = -44.72135955 + 2 x = -44.72135955 + 2 Combine like terms: -44.72135955 + 2 = -42.72135955 x = -42.72135955 Simplifying x = -42.72135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.72135955, -42.72135955}
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