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Simplifying 15x6 + 45x4 + -20x2 = 0 Reorder the terms: -20x2 + 45x4 + 15x6 = 0 Solving -20x2 + 45x4 + 15x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x2'. 5x2(-4 + 9x2 + 3x4) = 0 Ignore the factor 5.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 '(-4 + 9x2 + 3x4)' equal to zero and attempt to solve: Simplifying -4 + 9x2 + 3x4 = 0 Solving -4 + 9x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 3x2 + x4 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 3x2 + 1.333333333 + x4 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 3x2 + x4 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 3x2 + x4 = 0 + 1.333333333 3x2 + x4 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 3x2 + x4 = 1.333333333 The x term is 3x2. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x2 + 2.25 + x4 = 1.333333333 + 2.25 Reorder the terms: 2.25 + 3x2 + x4 = 1.333333333 + 2.25 Combine like terms: 1.333333333 + 2.25 = 3.583333333 2.25 + 3x2 + x4 = 3.583333333 Factor a perfect square on the left side: (x2 + 1.5)(x2 + 1.5) = 3.583333333 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (x2 + 1.5) equal to 1.892969449 and -1.892969449.Subproblem 1
x2 + 1.5 = 1.892969449 Simplifying x2 + 1.5 = 1.892969449 Reorder the terms: 1.5 + x2 = 1.892969449 Solving 1.5 + x2 = 1.892969449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = 1.892969449 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = 1.892969449 + -1.5 x2 = 1.892969449 + -1.5 Combine like terms: 1.892969449 + -1.5 = 0.392969449 x2 = 0.392969449 Simplifying x2 = 0.392969449 Take the square root of each side: x = {-0.626872753, 0.626872753}Subproblem 2
x2 + 1.5 = -1.892969449 Simplifying x2 + 1.5 = -1.892969449 Reorder the terms: 1.5 + x2 = -1.892969449 Solving 1.5 + x2 = -1.892969449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = -1.892969449 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = -1.892969449 + -1.5 x2 = -1.892969449 + -1.5 Combine like terms: -1.892969449 + -1.5 = -3.392969449 x2 = -3.392969449 Simplifying x2 = -3.392969449 Reorder the terms: 3.392969449 + x2 = -3.392969449 + 3.392969449 Combine like terms: -3.392969449 + 3.392969449 = 0.000000000 3.392969449 + 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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