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Simplifying 5x5 + 3x3 + x = 0 Reorder the terms: x + 3x3 + 5x5 = 0 Solving x + 3x3 + 5x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 3x2 + 5x4) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + 3x2 + 5x4)' equal to zero and attempt to solve: Simplifying 1 + 3x2 + 5x4 = 0 Solving 1 + 3x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 0.6x2 + x4 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 0.6x2 + -0.2 + x4 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 0.6x2 + x4 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 0.6x2 + x4 = 0 + -0.2 0.6x2 + x4 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 0.6x2 + x4 = -0.2 The x term is 0.6x2. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x2 + 0.09 + x4 = -0.2 + 0.09 Reorder the terms: 0.09 + 0.6x2 + x4 = -0.2 + 0.09 Combine like terms: -0.2 + 0.09 = -0.11 0.09 + 0.6x2 + x4 = -0.11 Factor a perfect square on the left side: (x2 + 0.3)(x2 + 0.3) = -0.11 Can't calculate square root of the right side. 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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