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Simplifying x2 + -128x + 3 = 0 Reorder the terms: 3 + -128x + x2 = 0 Solving 3 + -128x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -128x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -128x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -128x + x2 = 0 + -3 -128x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -128x + x2 = -3 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 = -3 + 4096 Reorder the terms: 4096 + -128x + x2 = -3 + 4096 Combine like terms: -3 + 4096 = 4093 4096 + -128x + x2 = 4093 Factor a perfect square on the left side: (x + -64)(x + -64) = 4093 Calculate the square root of the right side: 63.976558207 Break this problem into two subproblems by setting (x + -64) equal to 63.976558207 and -63.976558207.Subproblem 1
x + -64 = 63.976558207 Simplifying x + -64 = 63.976558207 Reorder the terms: -64 + x = 63.976558207 Solving -64 + x = 63.976558207 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 = 63.976558207 + 64 Combine like terms: -64 + 64 = 0 0 + x = 63.976558207 + 64 x = 63.976558207 + 64 Combine like terms: 63.976558207 + 64 = 127.976558207 x = 127.976558207 Simplifying x = 127.976558207Subproblem 2
x + -64 = -63.976558207 Simplifying x + -64 = -63.976558207 Reorder the terms: -64 + x = -63.976558207 Solving -64 + x = -63.976558207 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 = -63.976558207 + 64 Combine like terms: -64 + 64 = 0 0 + x = -63.976558207 + 64 x = -63.976558207 + 64 Combine like terms: -63.976558207 + 64 = 0.023441793 x = 0.023441793 Simplifying x = 0.023441793Solution
The solution to the problem is based on the solutions from the subproblems. x = {127.976558207, 0.023441793}
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