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Simplifying x2 + 4x + -256 = 0 Reorder the terms: -256 + 4x + x2 = 0 Solving -256 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '256' to each side of the equation. -256 + 4x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + 4x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 4x + x2 = 0 + 256 4x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 4x + x2 = 256 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 = 256 + 4 Reorder the terms: 4 + 4x + x2 = 256 + 4 Combine like terms: 256 + 4 = 260 4 + 4x + x2 = 260 Factor a perfect square on the left side: (x + 2)(x + 2) = 260 Calculate the square root of the right side: 16.124515497 Break this problem into two subproblems by setting (x + 2) equal to 16.124515497 and -16.124515497.Subproblem 1
x + 2 = 16.124515497 Simplifying x + 2 = 16.124515497 Reorder the terms: 2 + x = 16.124515497 Solving 2 + x = 16.124515497 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 = 16.124515497 + -2 Combine like terms: 2 + -2 = 0 0 + x = 16.124515497 + -2 x = 16.124515497 + -2 Combine like terms: 16.124515497 + -2 = 14.124515497 x = 14.124515497 Simplifying x = 14.124515497Subproblem 2
x + 2 = -16.124515497 Simplifying x + 2 = -16.124515497 Reorder the terms: 2 + x = -16.124515497 Solving 2 + x = -16.124515497 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 = -16.124515497 + -2 Combine like terms: 2 + -2 = 0 0 + x = -16.124515497 + -2 x = -16.124515497 + -2 Combine like terms: -16.124515497 + -2 = -18.124515497 x = -18.124515497 Simplifying x = -18.124515497Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.124515497, -18.124515497}
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