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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 = 16.246211251 x2 = 16.246211251 Simplifying x2 = 16.246211251 Take the square root of each side: x = {-4.03065891, 4.03065891}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 = -0.246211251 x2 = -0.246211251 Simplifying x2 = -0.246211251 Reorder the terms: 0.246211251 + x2 = -0.246211251 + 0.246211251 Combine like terms: -0.246211251 + 0.246211251 = 0.000000000 0.246211251 + 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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