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Simplifying -10x5 + -4x3 + 8x = 0 Reorder the terms: 8x + -4x3 + -10x5 = 0 Solving 8x + -4x3 + -10x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(4 + -2x2 + -5x4) = 0 Ignore the factor 2.Subproblem 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 '(4 + -2x2 + -5x4)' equal to zero and attempt to solve: Simplifying 4 + -2x2 + -5x4 = 0 Solving 4 + -2x2 + -5x4 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.8 + 0.4x2 + x4 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.4x2 + 0.8 + x4 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.4x2 + x4 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.4x2 + x4 = 0 + 0.8 0.4x2 + x4 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.4x2 + x4 = 0.8 The x term is 0.4x2. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x2 + 0.04 + x4 = 0.8 + 0.04 Reorder the terms: 0.04 + 0.4x2 + x4 = 0.8 + 0.04 Combine like terms: 0.8 + 0.04 = 0.84 0.04 + 0.4x2 + x4 = 0.84 Factor a perfect square on the left side: (x2 + 0.2)(x2 + 0.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (x2 + 0.2) equal to 0.916515139 and -0.916515139.Subproblem 1
x2 + 0.2 = 0.916515139 Simplifying x2 + 0.2 = 0.916515139 Reorder the terms: 0.2 + x2 = 0.916515139 Solving 0.2 + x2 = 0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x2 = 0.916515139 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x2 = 0.916515139 + -0.2 x2 = 0.916515139 + -0.2 Combine like terms: 0.916515139 + -0.2 = 0.716515139 x2 = 0.716515139 Simplifying x2 = 0.716515139 Take the square root of each side: x = {-0.846472173, 0.846472173}Subproblem 2
x2 + 0.2 = -0.916515139 Simplifying x2 + 0.2 = -0.916515139 Reorder the terms: 0.2 + x2 = -0.916515139 Solving 0.2 + x2 = -0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x2 = -0.916515139 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x2 = -0.916515139 + -0.2 x2 = -0.916515139 + -0.2 Combine like terms: -0.916515139 + -0.2 = -1.116515139 x2 = -1.116515139 Simplifying x2 = -1.116515139 Reorder the terms: 1.116515139 + x2 = -1.116515139 + 1.116515139 Combine like terms: -1.116515139 + 1.116515139 = 0.000000000 1.116515139 + 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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