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Simplifying x5 + -6x3 + 2x = 0 Reorder the terms: 2x + -6x3 + x5 = 0 Solving 2x + -6x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(2 + -6x2 + x4) = 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 '(2 + -6x2 + x4)' equal to zero and attempt to solve: Simplifying 2 + -6x2 + x4 = 0 Solving 2 + -6x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6x2 + -2 + x4 = 0 + -2 Reorder the terms: 2 + -2 + -6x2 + x4 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6x2 + x4 = 0 + -2 -6x2 + x4 = 0 + -2 Combine like terms: 0 + -2 = -2 -6x2 + x4 = -2 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = -2 + 9 Reorder the terms: 9 + -6x2 + x4 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6x2 + x4 = 7 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x2 + -3) equal to 2.645751311 and -2.645751311.Subproblem 1
x2 + -3 = 2.645751311 Simplifying x2 + -3 = 2.645751311 Reorder the terms: -3 + x2 = 2.645751311 Solving -3 + x2 = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 2.645751311 + 3 x2 = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 x2 = 5.645751311 Simplifying x2 = 5.645751311 Take the square root of each side: x = {-2.376078978, 2.376078978}Subproblem 2
x2 + -3 = -2.645751311 Simplifying x2 + -3 = -2.645751311 Reorder the terms: -3 + x2 = -2.645751311 Solving -3 + x2 = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -2.645751311 + 3 x2 = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 x2 = 0.354248689 Simplifying x2 = 0.354248689 Take the square root of each side: x = {-0.595187944, 0.595187944}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.376078978, 2.376078978, -0.595187944, 0.595187944}Solution
x = {0, -2.376078978, 2.376078978, -0.595187944, 0.595187944}
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