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Simplifying 4x4 + 64x2 + 64 = 0 Reorder the terms: 64 + 64x2 + 4x4 = 0 Solving 64 + 64x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(16 + 16x2 + x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(16 + 16x2 + x4)' equal to zero and attempt to solve: Simplifying 16 + 16x2 + x4 = 0 Solving 16 + 16x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 16x2 + -16 + x4 = 0 + -16 Reorder the terms: 16 + -16 + 16x2 + x4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 16x2 + x4 = 0 + -16 16x2 + x4 = 0 + -16 Combine like terms: 0 + -16 = -16 16x2 + x4 = -16 The x term is 16x2. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x2 + 64 + x4 = -16 + 64 Reorder the terms: 64 + 16x2 + x4 = -16 + 64 Combine like terms: -16 + 64 = 48 64 + 16x2 + x4 = 48 Factor a perfect square on the left side: (x2 + 8)(x2 + 8) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x2 + 8) equal to 6.92820323 and -6.92820323.Subproblem 1
x2 + 8 = 6.92820323 Simplifying x2 + 8 = 6.92820323 Reorder the terms: 8 + x2 = 6.92820323 Solving 8 + x2 = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x2 = 6.92820323 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = 6.92820323 + -8 x2 = 6.92820323 + -8 Combine like terms: 6.92820323 + -8 = -1.07179677 x2 = -1.07179677 Simplifying x2 = -1.07179677 Reorder the terms: 1.07179677 + x2 = -1.07179677 + 1.07179677 Combine like terms: -1.07179677 + 1.07179677 = 0.00000000 1.07179677 + x2 = 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
x2 + 8 = -6.92820323 Simplifying x2 + 8 = -6.92820323 Reorder the terms: 8 + x2 = -6.92820323 Solving 8 + x2 = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x2 = -6.92820323 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = -6.92820323 + -8 x2 = -6.92820323 + -8 Combine like terms: -6.92820323 + -8 = -14.92820323 x2 = -14.92820323 Simplifying x2 = -14.92820323 Reorder the terms: 14.92820323 + x2 = -14.92820323 + 14.92820323 Combine like terms: -14.92820323 + 14.92820323 = 0.00000000 14.92820323 + x2 = 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. 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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