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Simplifying x2 + -4x + -512 = 0 Reorder the terms: -512 + -4x + x2 = 0 Solving -512 + -4x + 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 + -4x + 512 + x2 = 0 + 512 Reorder the terms: -512 + 512 + -4x + x2 = 0 + 512 Combine like terms: -512 + 512 = 0 0 + -4x + x2 = 0 + 512 -4x + x2 = 0 + 512 Combine like terms: 0 + 512 = 512 -4x + x2 = 512 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 = 512 + 4 Reorder the terms: 4 + -4x + x2 = 512 + 4 Combine like terms: 512 + 4 = 516 4 + -4x + x2 = 516 Factor a perfect square on the left side: (x + -2)(x + -2) = 516 Calculate the square root of the right side: 22.715633383 Break this problem into two subproblems by setting (x + -2) equal to 22.715633383 and -22.715633383.Subproblem 1
x + -2 = 22.715633383 Simplifying x + -2 = 22.715633383 Reorder the terms: -2 + x = 22.715633383 Solving -2 + x = 22.715633383 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 = 22.715633383 + 2 Combine like terms: -2 + 2 = 0 0 + x = 22.715633383 + 2 x = 22.715633383 + 2 Combine like terms: 22.715633383 + 2 = 24.715633383 x = 24.715633383 Simplifying x = 24.715633383Subproblem 2
x + -2 = -22.715633383 Simplifying x + -2 = -22.715633383 Reorder the terms: -2 + x = -22.715633383 Solving -2 + x = -22.715633383 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 = -22.715633383 + 2 Combine like terms: -2 + 2 = 0 0 + x = -22.715633383 + 2 x = -22.715633383 + 2 Combine like terms: -22.715633383 + 2 = -20.715633383 x = -20.715633383 Simplifying x = -20.715633383Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.715633383, -20.715633383}
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