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Simplifying x2 + 128x + -256 = 0 Reorder the terms: -256 + 128x + x2 = 0 Solving -256 + 128x + 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 + 128x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + 128x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 128x + x2 = 0 + 256 128x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 128x + x2 = 256 The x term is 128x. Take half its coefficient (64). Square it (4096) and add it to both sides. Add '4096' to each side of the equation. 128x + 4096 + x2 = 256 + 4096 Reorder the terms: 4096 + 128x + x2 = 256 + 4096 Combine like terms: 256 + 4096 = 4352 4096 + 128x + x2 = 4352 Factor a perfect square on the left side: (x + 64)(x + 64) = 4352 Calculate the square root of the right side: 65.96969001 Break this problem into two subproblems by setting (x + 64) equal to 65.96969001 and -65.96969001.Subproblem 1
x + 64 = 65.96969001 Simplifying x + 64 = 65.96969001 Reorder the terms: 64 + x = 65.96969001 Solving 64 + x = 65.96969001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + -64 + x = 65.96969001 + -64 Combine like terms: 64 + -64 = 0 0 + x = 65.96969001 + -64 x = 65.96969001 + -64 Combine like terms: 65.96969001 + -64 = 1.96969001 x = 1.96969001 Simplifying x = 1.96969001Subproblem 2
x + 64 = -65.96969001 Simplifying x + 64 = -65.96969001 Reorder the terms: 64 + x = -65.96969001 Solving 64 + x = -65.96969001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + -64 + x = -65.96969001 + -64 Combine like terms: 64 + -64 = 0 0 + x = -65.96969001 + -64 x = -65.96969001 + -64 Combine like terms: -65.96969001 + -64 = -129.96969001 x = -129.96969001 Simplifying x = -129.96969001Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.96969001, -129.96969001}
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