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Simplifying 27x6 + -6x4 + -30x2 = 0 Reorder the terms: -30x2 + -6x4 + 27x6 = 0 Solving -30x2 + -6x4 + 27x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(-10 + -2x2 + 9x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-10 + -2x2 + 9x4)' equal to zero and attempt to solve: Simplifying -10 + -2x2 + 9x4 = 0 Solving -10 + -2x2 + 9x4 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + -0.2222222222x2 + x4 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -0.2222222222x2 + 1.111111111 + x4 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -0.2222222222x2 + x4 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -0.2222222222x2 + x4 = 0 + 1.111111111 -0.2222222222x2 + x4 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -0.2222222222x2 + x4 = 1.111111111 The x term is -0.2222222222x2. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222x2 + 0.01234567901 + x4 = 1.111111111 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x2 + x4 = 1.111111111 + 0.01234567901 Combine like terms: 1.111111111 + 0.01234567901 = 1.12345679001 0.01234567901 + -0.2222222222x2 + x4 = 1.12345679001 Factor a perfect square on the left side: (x2 + -0.1111111111)(x2 + -0.1111111111) = 1.12345679001 Calculate the square root of the right side: 1.059932446 Break this problem into two subproblems by setting (x2 + -0.1111111111) equal to 1.059932446 and -1.059932446.Subproblem 1
x2 + -0.1111111111 = 1.059932446 Simplifying x2 + -0.1111111111 = 1.059932446 Reorder the terms: -0.1111111111 + x2 = 1.059932446 Solving -0.1111111111 + x2 = 1.059932446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x2 = 1.059932446 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x2 = 1.059932446 + 0.1111111111 x2 = 1.059932446 + 0.1111111111 Combine like terms: 1.059932446 + 0.1111111111 = 1.1710435571 x2 = 1.1710435571 Simplifying x2 = 1.1710435571 Take the square root of each side: x = {-1.08214766, 1.08214766}Subproblem 2
x2 + -0.1111111111 = -1.059932446 Simplifying x2 + -0.1111111111 = -1.059932446 Reorder the terms: -0.1111111111 + x2 = -1.059932446 Solving -0.1111111111 + x2 = -1.059932446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x2 = -1.059932446 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x2 = -1.059932446 + 0.1111111111 x2 = -1.059932446 + 0.1111111111 Combine like terms: -1.059932446 + 0.1111111111 = -0.9488213349 x2 = -0.9488213349 Simplifying x2 = -0.9488213349 Reorder the terms: 0.9488213349 + x2 = -0.9488213349 + 0.9488213349 Combine like terms: -0.9488213349 + 0.9488213349 = 0.0000000000 0.9488213349 + x2 = 0.0000000000 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. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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