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Simplifying x6 + 64x3 + 64 = 0 Reorder the terms: 64 + 64x3 + x6 = 0 Solving 64 + 64x3 + x6 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + 64x3 + -64 + x6 = 0 + -64 Reorder the terms: 64 + -64 + 64x3 + x6 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + 64x3 + x6 = 0 + -64 64x3 + x6 = 0 + -64 Combine like terms: 0 + -64 = -64 64x3 + x6 = -64 The x term is 64x3. Take half its coefficient (32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. 64x3 + 1024 + x6 = -64 + 1024 Reorder the terms: 1024 + 64x3 + x6 = -64 + 1024 Combine like terms: -64 + 1024 = 960 1024 + 64x3 + x6 = 960 Factor a perfect square on the left side: (x3 + 32)(x3 + 32) = 960 Calculate the square root of the right side: 30.98386677 Break this problem into two subproblems by setting (x3 + 32) equal to 30.98386677 and -30.98386677.Subproblem 1
x3 + 32 = 30.98386677 Simplifying x3 + 32 = 30.98386677 Reorder the terms: 32 + x3 = 30.98386677 Solving 32 + x3 = 30.98386677 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 + x3 = 30.98386677 + -32 Combine like terms: 32 + -32 = 0 0 + x3 = 30.98386677 + -32 x3 = 30.98386677 + -32 Combine like terms: 30.98386677 + -32 = -1.01613323 x3 = -1.01613323 Simplifying x3 = -1.01613323 Reorder the terms: 1.01613323 + x3 = -1.01613323 + 1.01613323 Combine like terms: -1.01613323 + 1.01613323 = 0.00000000 1.01613323 + x3 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + 32 = -30.98386677 Simplifying x3 + 32 = -30.98386677 Reorder the terms: 32 + x3 = -30.98386677 Solving 32 + x3 = -30.98386677 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 + x3 = -30.98386677 + -32 Combine like terms: 32 + -32 = 0 0 + x3 = -30.98386677 + -32 x3 = -30.98386677 + -32 Combine like terms: -30.98386677 + -32 = -62.98386677 x3 = -62.98386677 Simplifying x3 = -62.98386677 Reorder the terms: 62.98386677 + x3 = -62.98386677 + 62.98386677 Combine like terms: -62.98386677 + 62.98386677 = 0.00000000 62.98386677 + x3 = 0.00000000 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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