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Simplifying X2 + -32760X = 1296 Reorder the terms: -32760X + X2 = 1296 Solving -32760X + X2 = 1296 Solving for variable 'X'. Reorder the terms: -1296 + -32760X + X2 = 1296 + -1296 Combine like terms: 1296 + -1296 = 0 -1296 + -32760X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '1296' to each side of the equation. -1296 + -32760X + 1296 + X2 = 0 + 1296 Reorder the terms: -1296 + 1296 + -32760X + X2 = 0 + 1296 Combine like terms: -1296 + 1296 = 0 0 + -32760X + X2 = 0 + 1296 -32760X + X2 = 0 + 1296 Combine like terms: 0 + 1296 = 1296 -32760X + X2 = 1296 The X term is -32760X. Take half its coefficient (-16380). Square it (268304400) and add it to both sides. Add '268304400' to each side of the equation. -32760X + 268304400 + X2 = 1296 + 268304400 Reorder the terms: 268304400 + -32760X + X2 = 1296 + 268304400 Combine like terms: 1296 + 268304400 = 268305696 268304400 + -32760X + X2 = 268305696 Factor a perfect square on the left side: (X + -16380)(X + -16380) = 268305696 Calculate the square root of the right side: 16380.039560392 Break this problem into two subproblems by setting (X + -16380) equal to 16380.039560392 and -16380.039560392.Subproblem 1
X + -16380 = 16380.039560392 Simplifying X + -16380 = 16380.039560392 Reorder the terms: -16380 + X = 16380.039560392 Solving -16380 + X = 16380.039560392 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '16380' to each side of the equation. -16380 + 16380 + X = 16380.039560392 + 16380 Combine like terms: -16380 + 16380 = 0 0 + X = 16380.039560392 + 16380 X = 16380.039560392 + 16380 Combine like terms: 16380.039560392 + 16380 = 32760.039560392 X = 32760.039560392 Simplifying X = 32760.039560392Subproblem 2
X + -16380 = -16380.039560392 Simplifying X + -16380 = -16380.039560392 Reorder the terms: -16380 + X = -16380.039560392 Solving -16380 + X = -16380.039560392 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '16380' to each side of the equation. -16380 + 16380 + X = -16380.039560392 + 16380 Combine like terms: -16380 + 16380 = 0 0 + X = -16380.039560392 + 16380 X = -16380.039560392 + 16380 Combine like terms: -16380.039560392 + 16380 = -0.039560392 X = -0.039560392 Simplifying X = -0.039560392Solution
The solution to the problem is based on the solutions from the subproblems. X = {32760.039560392, -0.039560392}
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