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Simplifying x4 + -16x2 + -39 = 0 Reorder the terms: -39 + -16x2 + x4 = 0 Solving -39 + -16x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -16x2 + 39 + x4 = 0 + 39 Reorder the terms: -39 + 39 + -16x2 + x4 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -16x2 + x4 = 0 + 39 -16x2 + x4 = 0 + 39 Combine like terms: 0 + 39 = 39 -16x2 + x4 = 39 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 = 39 + 64 Reorder the terms: 64 + -16x2 + x4 = 39 + 64 Combine like terms: 39 + 64 = 103 64 + -16x2 + x4 = 103 Factor a perfect square on the left side: (x2 + -8)(x2 + -8) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (x2 + -8) equal to 10.148891565 and -10.148891565.Subproblem 1
x2 + -8 = 10.148891565 Simplifying x2 + -8 = 10.148891565 Reorder the terms: -8 + x2 = 10.148891565 Solving -8 + x2 = 10.148891565 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 = 10.148891565 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 10.148891565 + 8 x2 = 10.148891565 + 8 Combine like terms: 10.148891565 + 8 = 18.148891565 x2 = 18.148891565 Simplifying x2 = 18.148891565 Take the square root of each side: x = {-4.260151589, 4.260151589}Subproblem 2
x2 + -8 = -10.148891565 Simplifying x2 + -8 = -10.148891565 Reorder the terms: -8 + x2 = -10.148891565 Solving -8 + x2 = -10.148891565 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 = -10.148891565 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = -10.148891565 + 8 x2 = -10.148891565 + 8 Combine like terms: -10.148891565 + 8 = -2.148891565 x2 = -2.148891565 Simplifying x2 = -2.148891565 Reorder the terms: 2.148891565 + x2 = -2.148891565 + 2.148891565 Combine like terms: -2.148891565 + 2.148891565 = 0.000000000 2.148891565 + 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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