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Simplifying x4 + 16x2 = 4 Reorder the terms: 16x2 + x4 = 4 Solving 16x2 + x4 = 4 Solving for variable 'x'. Reorder the terms: -4 + 16x2 + x4 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 16x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 16x2 + 4 + x4 = 0 + 4 Reorder the terms: -4 + 4 + 16x2 + x4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 16x2 + x4 = 0 + 4 16x2 + x4 = 0 + 4 Combine like terms: 0 + 4 = 4 16x2 + x4 = 4 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 = 4 + 64 Reorder the terms: 64 + 16x2 + x4 = 4 + 64 Combine like terms: 4 + 64 = 68 64 + 16x2 + x4 = 68 Factor a perfect square on the left side: (x2 + 8)(x2 + 8) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (x2 + 8) equal to 8.246211251 and -8.246211251.Subproblem 1
x2 + 8 = 8.246211251 Simplifying x2 + 8 = 8.246211251 Reorder the terms: 8 + x2 = 8.246211251 Solving 8 + x2 = 8.246211251 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 = 8.246211251 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = 8.246211251 + -8 x2 = 8.246211251 + -8 Combine like terms: 8.246211251 + -8 = 0.246211251 x2 = 0.246211251 Simplifying x2 = 0.246211251 Take the square root of each side: x = {-0.496196787, 0.496196787}Subproblem 2
x2 + 8 = -8.246211251 Simplifying x2 + 8 = -8.246211251 Reorder the terms: 8 + x2 = -8.246211251 Solving 8 + x2 = -8.246211251 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 = -8.246211251 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = -8.246211251 + -8 x2 = -8.246211251 + -8 Combine like terms: -8.246211251 + -8 = -16.246211251 x2 = -16.246211251 Simplifying x2 = -16.246211251 Reorder the terms: 16.246211251 + x2 = -16.246211251 + 16.246211251 Combine like terms: -16.246211251 + 16.246211251 = 0.000000000 16.246211251 + 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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