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Simplifying x4 + 8x2 + 10 = 0 Reorder the terms: 10 + 8x2 + x4 = 0 Solving 10 + 8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 8x2 + -10 + x4 = 0 + -10 Reorder the terms: 10 + -10 + 8x2 + x4 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 8x2 + x4 = 0 + -10 8x2 + x4 = 0 + -10 Combine like terms: 0 + -10 = -10 8x2 + x4 = -10 The x term is 8x2. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x2 + 16 + x4 = -10 + 16 Reorder the terms: 16 + 8x2 + x4 = -10 + 16 Combine like terms: -10 + 16 = 6 16 + 8x2 + x4 = 6 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x2 + 4) equal to 2.449489743 and -2.449489743.Subproblem 1
x2 + 4 = 2.449489743 Simplifying x2 + 4 = 2.449489743 Reorder the terms: 4 + x2 = 2.449489743 Solving 4 + x2 = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = 2.449489743 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 2.449489743 + -4 x2 = 2.449489743 + -4 Combine like terms: 2.449489743 + -4 = -1.550510257 x2 = -1.550510257 Simplifying x2 = -1.550510257 Reorder the terms: 1.550510257 + x2 = -1.550510257 + 1.550510257 Combine like terms: -1.550510257 + 1.550510257 = 0.000000000 1.550510257 + 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 + 4 = -2.449489743 Simplifying x2 + 4 = -2.449489743 Reorder the terms: 4 + x2 = -2.449489743 Solving 4 + x2 = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = -2.449489743 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -2.449489743 + -4 x2 = -2.449489743 + -4 Combine like terms: -2.449489743 + -4 = -6.449489743 x2 = -6.449489743 Simplifying x2 = -6.449489743 Reorder the terms: 6.449489743 + x2 = -6.449489743 + 6.449489743 Combine like terms: -6.449489743 + 6.449489743 = 0.000000000 6.449489743 + 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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