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Simplifying x5 + -17x3 + 6x = 0 Reorder the terms: 6x + -17x3 + x5 = 0 Solving 6x + -17x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(6 + -17x2 + 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 '(6 + -17x2 + x4)' equal to zero and attempt to solve: Simplifying 6 + -17x2 + x4 = 0 Solving 6 + -17x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -17x2 + -6 + x4 = 0 + -6 Reorder the terms: 6 + -6 + -17x2 + x4 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -17x2 + x4 = 0 + -6 -17x2 + x4 = 0 + -6 Combine like terms: 0 + -6 = -6 -17x2 + x4 = -6 The x term is -17x2. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x2 + 72.25 + x4 = -6 + 72.25 Reorder the terms: 72.25 + -17x2 + x4 = -6 + 72.25 Combine like terms: -6 + 72.25 = 66.25 72.25 + -17x2 + x4 = 66.25 Factor a perfect square on the left side: (x2 + -8.5)(x2 + -8.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (x2 + -8.5) equal to 8.139410298 and -8.139410298.Subproblem 1
x2 + -8.5 = 8.139410298 Simplifying x2 + -8.5 = 8.139410298 Reorder the terms: -8.5 + x2 = 8.139410298 Solving -8.5 + x2 = 8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x2 = 8.139410298 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x2 = 8.139410298 + 8.5 x2 = 8.139410298 + 8.5 Combine like terms: 8.139410298 + 8.5 = 16.639410298 x2 = 16.639410298 Simplifying x2 = 16.639410298 Take the square root of each side: x = {-4.079143329, 4.079143329}Subproblem 2
x2 + -8.5 = -8.139410298 Simplifying x2 + -8.5 = -8.139410298 Reorder the terms: -8.5 + x2 = -8.139410298 Solving -8.5 + x2 = -8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x2 = -8.139410298 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x2 = -8.139410298 + 8.5 x2 = -8.139410298 + 8.5 Combine like terms: -8.139410298 + 8.5 = 0.360589702 x2 = 0.360589702 Simplifying x2 = 0.360589702 Take the square root of each side: x = {-0.600491217, 0.600491217}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.079143329, 4.079143329, -0.600491217, 0.600491217}Solution
x = {0, -4.079143329, 4.079143329, -0.600491217, 0.600491217}
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