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Simplifying 4x5 + -112x3 + -54x = 0 Reorder the terms: -54x + -112x3 + 4x5 = 0 Solving -54x + -112x3 + 4x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-27 + -56x2 + 2x4) = 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 '(-27 + -56x2 + 2x4)' equal to zero and attempt to solve: Simplifying -27 + -56x2 + 2x4 = 0 Solving -27 + -56x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + -28x2 + x4 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -28x2 + 13.5 + x4 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -28x2 + x4 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -28x2 + x4 = 0 + 13.5 -28x2 + x4 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -28x2 + x4 = 13.5 The x term is -28x2. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x2 + 196 + x4 = 13.5 + 196 Reorder the terms: 196 + -28x2 + x4 = 13.5 + 196 Combine like terms: 13.5 + 196 = 209.5 196 + -28x2 + x4 = 209.5 Factor a perfect square on the left side: (x2 + -14)(x2 + -14) = 209.5 Calculate the square root of the right side: 14.474114826 Break this problem into two subproblems by setting (x2 + -14) equal to 14.474114826 and -14.474114826.Subproblem 1
x2 + -14 = 14.474114826 Simplifying x2 + -14 = 14.474114826 Reorder the terms: -14 + x2 = 14.474114826 Solving -14 + x2 = 14.474114826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x2 = 14.474114826 + 14 Combine like terms: -14 + 14 = 0 0 + x2 = 14.474114826 + 14 x2 = 14.474114826 + 14 Combine like terms: 14.474114826 + 14 = 28.474114826 x2 = 28.474114826 Simplifying x2 = 28.474114826 Take the square root of each side: x = {-5.336114207, 5.336114207}Subproblem 2
x2 + -14 = -14.474114826 Simplifying x2 + -14 = -14.474114826 Reorder the terms: -14 + x2 = -14.474114826 Solving -14 + x2 = -14.474114826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x2 = -14.474114826 + 14 Combine like terms: -14 + 14 = 0 0 + x2 = -14.474114826 + 14 x2 = -14.474114826 + 14 Combine like terms: -14.474114826 + 14 = -0.474114826 x2 = -0.474114826 Simplifying x2 = -0.474114826 Reorder the terms: 0.474114826 + x2 = -0.474114826 + 0.474114826 Combine like terms: -0.474114826 + 0.474114826 = 0.000000000 0.474114826 + 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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