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Simplifying (x2) + 128x + 126 = 0 x2 + 128x + 126 = 0 Reorder the terms: 126 + 128x + x2 = 0 Solving 126 + 128x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-126' to each side of the equation. 126 + 128x + -126 + x2 = 0 + -126 Reorder the terms: 126 + -126 + 128x + x2 = 0 + -126 Combine like terms: 126 + -126 = 0 0 + 128x + x2 = 0 + -126 128x + x2 = 0 + -126 Combine like terms: 0 + -126 = -126 128x + x2 = -126 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 = -126 + 4096 Reorder the terms: 4096 + 128x + x2 = -126 + 4096 Combine like terms: -126 + 4096 = 3970 4096 + 128x + x2 = 3970 Factor a perfect square on the left side: (x + 64)(x + 64) = 3970 Calculate the square root of the right side: 63.007936008 Break this problem into two subproblems by setting (x + 64) equal to 63.007936008 and -63.007936008.Subproblem 1
x + 64 = 63.007936008 Simplifying x + 64 = 63.007936008 Reorder the terms: 64 + x = 63.007936008 Solving 64 + x = 63.007936008 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 = 63.007936008 + -64 Combine like terms: 64 + -64 = 0 0 + x = 63.007936008 + -64 x = 63.007936008 + -64 Combine like terms: 63.007936008 + -64 = -0.992063992 x = -0.992063992 Simplifying x = -0.992063992Subproblem 2
x + 64 = -63.007936008 Simplifying x + 64 = -63.007936008 Reorder the terms: 64 + x = -63.007936008 Solving 64 + x = -63.007936008 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 = -63.007936008 + -64 Combine like terms: 64 + -64 = 0 0 + x = -63.007936008 + -64 x = -63.007936008 + -64 Combine like terms: -63.007936008 + -64 = -127.007936008 x = -127.007936008 Simplifying x = -127.007936008Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.992063992, -127.007936008}
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