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Simplifying 81x4 + 9x2 + 1 = 0 Reorder the terms: 1 + 9x2 + 81x4 = 0 Solving 1 + 9x2 + 81x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. 0.01234567901 + 0.1111111111x2 + x4 = 0 Move the constant term to the right: Add '-0.01234567901' to each side of the equation. 0.01234567901 + 0.1111111111x2 + -0.01234567901 + x4 = 0 + -0.01234567901 Reorder the terms: 0.01234567901 + -0.01234567901 + 0.1111111111x2 + x4 = 0 + -0.01234567901 Combine like terms: 0.01234567901 + -0.01234567901 = 0.00000000000 0.00000000000 + 0.1111111111x2 + x4 = 0 + -0.01234567901 0.1111111111x2 + x4 = 0 + -0.01234567901 Combine like terms: 0 + -0.01234567901 = -0.01234567901 0.1111111111x2 + x4 = -0.01234567901 The x term is 0.1111111111x2. Take half its coefficient (0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. 0.1111111111x2 + 0.003086419752 + x4 = -0.01234567901 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111x2 + x4 = -0.01234567901 + 0.003086419752 Combine like terms: -0.01234567901 + 0.003086419752 = -0.009259259258 0.003086419752 + 0.1111111111x2 + x4 = -0.009259259258 Factor a perfect square on the left side: (x2 + 0.05555555555)(x2 + 0.05555555555) = -0.009259259258 Can't calculate square root of the right side. The solution to this equation could not be determined.
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