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Simplifying x4 + 64x2 + -729 = 0 Reorder the terms: -729 + 64x2 + x4 = 0 Solving -729 + 64x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '729' to each side of the equation. -729 + 64x2 + 729 + x4 = 0 + 729 Reorder the terms: -729 + 729 + 64x2 + x4 = 0 + 729 Combine like terms: -729 + 729 = 0 0 + 64x2 + x4 = 0 + 729 64x2 + x4 = 0 + 729 Combine like terms: 0 + 729 = 729 64x2 + x4 = 729 The x term is 64x2. Take half its coefficient (32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. 64x2 + 1024 + x4 = 729 + 1024 Reorder the terms: 1024 + 64x2 + x4 = 729 + 1024 Combine like terms: 729 + 1024 = 1753 1024 + 64x2 + x4 = 1753 Factor a perfect square on the left side: (x2 + 32)(x2 + 32) = 1753 Calculate the square root of the right side: 41.868842831 Break this problem into two subproblems by setting (x2 + 32) equal to 41.868842831 and -41.868842831.Subproblem 1
x2 + 32 = 41.868842831 Simplifying x2 + 32 = 41.868842831 Reorder the terms: 32 + x2 = 41.868842831 Solving 32 + x2 = 41.868842831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x2 = 41.868842831 + -32 Combine like terms: 32 + -32 = 0 0 + x2 = 41.868842831 + -32 x2 = 41.868842831 + -32 Combine like terms: 41.868842831 + -32 = 9.868842831 x2 = 9.868842831 Simplifying x2 = 9.868842831 Take the square root of each side: x = {-3.141471444, 3.141471444}Subproblem 2
x2 + 32 = -41.868842831 Simplifying x2 + 32 = -41.868842831 Reorder the terms: 32 + x2 = -41.868842831 Solving 32 + x2 = -41.868842831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x2 = -41.868842831 + -32 Combine like terms: 32 + -32 = 0 0 + x2 = -41.868842831 + -32 x2 = -41.868842831 + -32 Combine like terms: -41.868842831 + -32 = -73.868842831 x2 = -73.868842831 Simplifying x2 = -73.868842831 Reorder the terms: 73.868842831 + x2 = -73.868842831 + 73.868842831 Combine like terms: -73.868842831 + 73.868842831 = 0.000000000 73.868842831 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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