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Simplifying 40x5 + 32x + 25x3 = 0 Reorder the terms: 32x + 25x3 + 40x5 = 0 Solving 32x + 25x3 + 40x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(32 + 25x2 + 40x4) = 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 '(32 + 25x2 + 40x4)' equal to zero and attempt to solve: Simplifying 32 + 25x2 + 40x4 = 0 Solving 32 + 25x2 + 40x4 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. 0.8 + 0.625x2 + x4 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 0.625x2 + -0.8 + x4 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 0.625x2 + x4 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 0.625x2 + x4 = 0 + -0.8 0.625x2 + x4 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 0.625x2 + x4 = -0.8 The x term is 0.625x2. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x2 + 0.09765625 + x4 = -0.8 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x2 + x4 = -0.8 + 0.09765625 Combine like terms: -0.8 + 0.09765625 = -0.70234375 0.09765625 + 0.625x2 + x4 = -0.70234375 Factor a perfect square on the left side: (x2 + 0.3125)(x2 + 0.3125) = -0.70234375 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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