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Simplifying x2 + -2x + -512 = 0 Reorder the terms: -512 + -2x + x2 = 0 Solving -512 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '512' to each side of the equation. -512 + -2x + 512 + x2 = 0 + 512 Reorder the terms: -512 + 512 + -2x + x2 = 0 + 512 Combine like terms: -512 + 512 = 0 0 + -2x + x2 = 0 + 512 -2x + x2 = 0 + 512 Combine like terms: 0 + 512 = 512 -2x + x2 = 512 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 512 + 1 Reorder the terms: 1 + -2x + x2 = 512 + 1 Combine like terms: 512 + 1 = 513 1 + -2x + x2 = 513 Factor a perfect square on the left side: (x + -1)(x + -1) = 513 Calculate the square root of the right side: 22.649503306 Break this problem into two subproblems by setting (x + -1) equal to 22.649503306 and -22.649503306.Subproblem 1
x + -1 = 22.649503306 Simplifying x + -1 = 22.649503306 Reorder the terms: -1 + x = 22.649503306 Solving -1 + x = 22.649503306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 22.649503306 + 1 Combine like terms: -1 + 1 = 0 0 + x = 22.649503306 + 1 x = 22.649503306 + 1 Combine like terms: 22.649503306 + 1 = 23.649503306 x = 23.649503306 Simplifying x = 23.649503306Subproblem 2
x + -1 = -22.649503306 Simplifying x + -1 = -22.649503306 Reorder the terms: -1 + x = -22.649503306 Solving -1 + x = -22.649503306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -22.649503306 + 1 Combine like terms: -1 + 1 = 0 0 + x = -22.649503306 + 1 x = -22.649503306 + 1 Combine like terms: -22.649503306 + 1 = -21.649503306 x = -21.649503306 Simplifying x = -21.649503306Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.649503306, -21.649503306}
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