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Simplifying x5 + 20x3 + -100x = 0 Reorder the terms: -100x + 20x3 + x5 = 0 Solving -100x + 20x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-100 + 20x2 + 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 '(-100 + 20x2 + x4)' equal to zero and attempt to solve: Simplifying -100 + 20x2 + x4 = 0 Solving -100 + 20x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 20x2 + 100 + x4 = 0 + 100 Reorder the terms: -100 + 100 + 20x2 + x4 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 20x2 + x4 = 0 + 100 20x2 + x4 = 0 + 100 Combine like terms: 0 + 100 = 100 20x2 + x4 = 100 The x term is 20x2. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x2 + 100 + x4 = 100 + 100 Reorder the terms: 100 + 20x2 + x4 = 100 + 100 Combine like terms: 100 + 100 = 200 100 + 20x2 + x4 = 200 Factor a perfect square on the left side: (x2 + 10)(x2 + 10) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x2 + 10) equal to 14.142135624 and -14.142135624.Subproblem 1
x2 + 10 = 14.142135624 Simplifying x2 + 10 = 14.142135624 Reorder the terms: 10 + x2 = 14.142135624 Solving 10 + x2 = 14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x2 = 14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + x2 = 14.142135624 + -10 x2 = 14.142135624 + -10 Combine like terms: 14.142135624 + -10 = 4.142135624 x2 = 4.142135624 Simplifying x2 = 4.142135624 Take the square root of each side: x = {-2.035223728, 2.035223728}Subproblem 2
x2 + 10 = -14.142135624 Simplifying x2 + 10 = -14.142135624 Reorder the terms: 10 + x2 = -14.142135624 Solving 10 + x2 = -14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x2 = -14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + x2 = -14.142135624 + -10 x2 = -14.142135624 + -10 Combine like terms: -14.142135624 + -10 = -24.142135624 x2 = -24.142135624 Simplifying x2 = -24.142135624 Reorder the terms: 24.142135624 + x2 = -24.142135624 + 24.142135624 Combine like terms: -24.142135624 + 24.142135624 = 0.000000000 24.142135624 + 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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