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Simplifying x2 + x + -1728 = 0 Reorder the terms: -1728 + x + x2 = 0 Solving -1728 + x + 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 + x + 1728 + x2 = 0 + 1728 Reorder the terms: -1728 + 1728 + x + x2 = 0 + 1728 Combine like terms: -1728 + 1728 = 0 0 + x + x2 = 0 + 1728 x + x2 = 0 + 1728 Combine like terms: 0 + 1728 = 1728 x + x2 = 1728 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 1728 + 0.25 Reorder the terms: 0.25 + x + x2 = 1728 + 0.25 Combine like terms: 1728 + 0.25 = 1728.25 0.25 + x + x2 = 1728.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1728.25 Calculate the square root of the right side: 41.572226306 Break this problem into two subproblems by setting (x + 0.5) equal to 41.572226306 and -41.572226306.Subproblem 1
x + 0.5 = 41.572226306 Simplifying x + 0.5 = 41.572226306 Reorder the terms: 0.5 + x = 41.572226306 Solving 0.5 + x = 41.572226306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 41.572226306 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 41.572226306 + -0.5 x = 41.572226306 + -0.5 Combine like terms: 41.572226306 + -0.5 = 41.072226306 x = 41.072226306 Simplifying x = 41.072226306Subproblem 2
x + 0.5 = -41.572226306 Simplifying x + 0.5 = -41.572226306 Reorder the terms: 0.5 + x = -41.572226306 Solving 0.5 + x = -41.572226306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -41.572226306 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -41.572226306 + -0.5 x = -41.572226306 + -0.5 Combine like terms: -41.572226306 + -0.5 = -42.072226306 x = -42.072226306 Simplifying x = -42.072226306Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.072226306, -42.072226306}
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