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Simplifying X2 + -327680X = 1296 Reorder the terms: -327680X + X2 = 1296 Solving -327680X + X2 = 1296 Solving for variable 'X'. Reorder the terms: -1296 + -327680X + X2 = 1296 + -1296 Combine like terms: 1296 + -1296 = 0 -1296 + -327680X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '1296' to each side of the equation. -1296 + -327680X + 1296 + X2 = 0 + 1296 Reorder the terms: -1296 + 1296 + -327680X + X2 = 0 + 1296 Combine like terms: -1296 + 1296 = 0 0 + -327680X + X2 = 0 + 1296 -327680X + X2 = 0 + 1296 Combine like terms: 0 + 1296 = 1296 -327680X + X2 = 1296 The X term is -327680X. Take half its coefficient (-163840). Square it (26843545600) and add it to both sides. Add '26843545600' to each side of the equation. -327680X + 26843545600 + X2 = 1296 + 26843545600 Reorder the terms: 26843545600 + -327680X + X2 = 1296 + 26843545600 Combine like terms: 1296 + 26843545600 = 26843546896 26843545600 + -327680X + X2 = 26843546896 Factor a perfect square on the left side: (X + -163840)(X + -163840) = 26843546896 Calculate the square root of the right side: 163840.003955078 Break this problem into two subproblems by setting (X + -163840) equal to 163840.003955078 and -163840.003955078.Subproblem 1
X + -163840 = 163840.003955078 Simplifying X + -163840 = 163840.003955078 Reorder the terms: -163840 + X = 163840.003955078 Solving -163840 + X = 163840.003955078 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '163840' to each side of the equation. -163840 + 163840 + X = 163840.003955078 + 163840 Combine like terms: -163840 + 163840 = 0 0 + X = 163840.003955078 + 163840 X = 163840.003955078 + 163840 Combine like terms: 163840.003955078 + 163840 = 327680.003955078 X = 327680.003955078 Simplifying X = 327680.003955078Subproblem 2
X + -163840 = -163840.003955078 Simplifying X + -163840 = -163840.003955078 Reorder the terms: -163840 + X = -163840.003955078 Solving -163840 + X = -163840.003955078 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '163840' to each side of the equation. -163840 + 163840 + X = -163840.003955078 + 163840 Combine like terms: -163840 + 163840 = 0 0 + X = -163840.003955078 + 163840 X = -163840.003955078 + 163840 Combine like terms: -163840.003955078 + 163840 = -0.003955078 X = -0.003955078 Simplifying X = -0.003955078Solution
The solution to the problem is based on the solutions from the subproblems. X = {327680.003955078, -0.003955078}
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