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Simplifying x2 + 4x + -1728 = 0 Reorder the terms: -1728 + 4x + x2 = 0 Solving -1728 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1728' to each side of the equation. -1728 + 4x + 1728 + x2 = 0 + 1728 Reorder the terms: -1728 + 1728 + 4x + x2 = 0 + 1728 Combine like terms: -1728 + 1728 = 0 0 + 4x + x2 = 0 + 1728 4x + x2 = 0 + 1728 Combine like terms: 0 + 1728 = 1728 4x + x2 = 1728 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 = 1728 + 4 Reorder the terms: 4 + 4x + x2 = 1728 + 4 Combine like terms: 1728 + 4 = 1732 4 + 4x + x2 = 1732 Factor a perfect square on the left side: (x + 2)(x + 2) = 1732 Calculate the square root of the right side: 41.617304093 Break this problem into two subproblems by setting (x + 2) equal to 41.617304093 and -41.617304093.Subproblem 1
x + 2 = 41.617304093 Simplifying x + 2 = 41.617304093 Reorder the terms: 2 + x = 41.617304093 Solving 2 + x = 41.617304093 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 = 41.617304093 + -2 Combine like terms: 2 + -2 = 0 0 + x = 41.617304093 + -2 x = 41.617304093 + -2 Combine like terms: 41.617304093 + -2 = 39.617304093 x = 39.617304093 Simplifying x = 39.617304093Subproblem 2
x + 2 = -41.617304093 Simplifying x + 2 = -41.617304093 Reorder the terms: 2 + x = -41.617304093 Solving 2 + x = -41.617304093 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 = -41.617304093 + -2 Combine like terms: 2 + -2 = 0 0 + x = -41.617304093 + -2 x = -41.617304093 + -2 Combine like terms: -41.617304093 + -2 = -43.617304093 x = -43.617304093 Simplifying x = -43.617304093Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.617304093, -43.617304093}
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