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Simplifying x4 + 16x2 + 1 = 0 Reorder the terms: 1 + 16x2 + x4 = 0 Solving 1 + 16x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 16x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + 16x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 16x2 + x4 = 0 + -1 16x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 16x2 + x4 = -1 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 = -1 + 64 Reorder the terms: 64 + 16x2 + x4 = -1 + 64 Combine like terms: -1 + 64 = 63 64 + 16x2 + x4 = 63 Factor a perfect square on the left side: (x2 + 8)(x2 + 8) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x2 + 8) equal to 7.937253933 and -7.937253933.Subproblem 1
x2 + 8 = 7.937253933 Simplifying x2 + 8 = 7.937253933 Reorder the terms: 8 + x2 = 7.937253933 Solving 8 + x2 = 7.937253933 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 = 7.937253933 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = 7.937253933 + -8 x2 = 7.937253933 + -8 Combine like terms: 7.937253933 + -8 = -0.062746067 x2 = -0.062746067 Simplifying x2 = -0.062746067 Reorder the terms: 0.062746067 + x2 = -0.062746067 + 0.062746067 Combine like terms: -0.062746067 + 0.062746067 = 0.000000000 0.062746067 + x2 = 0.000000000 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 = -7.937253933 Simplifying x2 + 8 = -7.937253933 Reorder the terms: 8 + x2 = -7.937253933 Solving 8 + x2 = -7.937253933 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 = -7.937253933 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = -7.937253933 + -8 x2 = -7.937253933 + -8 Combine like terms: -7.937253933 + -8 = -15.937253933 x2 = -15.937253933 Simplifying x2 = -15.937253933 Reorder the terms: 15.937253933 + x2 = -15.937253933 + 15.937253933 Combine like terms: -15.937253933 + 15.937253933 = 0.000000000 15.937253933 + 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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