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Simplifying 36x4 + 84x2 + -18x6 = 0 Reorder the terms: 84x2 + 36x4 + -18x6 = 0 Solving 84x2 + 36x4 + -18x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x2'. 6x2(14 + 6x2 + -3x4) = 0 Ignore the factor 6.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 '(14 + 6x2 + -3x4)' equal to zero and attempt to solve: Simplifying 14 + 6x2 + -3x4 = 0 Solving 14 + 6x2 + -3x4 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -4.666666667 + -2x2 + x4 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + -2x2 + 4.666666667 + x4 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + -2x2 + x4 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + -2x2 + x4 = 0 + 4.666666667 -2x2 + x4 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 -2x2 + x4 = 4.666666667 The x term is -2x2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x2 + 1 + x4 = 4.666666667 + 1 Reorder the terms: 1 + -2x2 + x4 = 4.666666667 + 1 Combine like terms: 4.666666667 + 1 = 5.666666667 1 + -2x2 + x4 = 5.666666667 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 5.666666667 Calculate the square root of the right side: 2.380476143 Break this problem into two subproblems by setting (x2 + -1) equal to 2.380476143 and -2.380476143.Subproblem 1
x2 + -1 = 2.380476143 Simplifying x2 + -1 = 2.380476143 Reorder the terms: -1 + x2 = 2.380476143 Solving -1 + x2 = 2.380476143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = 2.380476143 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 2.380476143 + 1 x2 = 2.380476143 + 1 Combine like terms: 2.380476143 + 1 = 3.380476143 x2 = 3.380476143 Simplifying x2 = 3.380476143 Take the square root of each side: x = {-1.83860712, 1.83860712}Subproblem 2
x2 + -1 = -2.380476143 Simplifying x2 + -1 = -2.380476143 Reorder the terms: -1 + x2 = -2.380476143 Solving -1 + x2 = -2.380476143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = -2.380476143 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -2.380476143 + 1 x2 = -2.380476143 + 1 Combine like terms: -2.380476143 + 1 = -1.380476143 x2 = -1.380476143 Simplifying x2 = -1.380476143 Reorder the terms: 1.380476143 + x2 = -1.380476143 + 1.380476143 Combine like terms: -1.380476143 + 1.380476143 = 0.000000000 1.380476143 + 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. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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