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Simplifying x5 + -13x3 + 27x = 0 Reorder the terms: 27x + -13x3 + x5 = 0 Solving 27x + -13x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(27 + -13x2 + 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 '(27 + -13x2 + x4)' equal to zero and attempt to solve: Simplifying 27 + -13x2 + x4 = 0 Solving 27 + -13x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -13x2 + -27 + x4 = 0 + -27 Reorder the terms: 27 + -27 + -13x2 + x4 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -13x2 + x4 = 0 + -27 -13x2 + x4 = 0 + -27 Combine like terms: 0 + -27 = -27 -13x2 + x4 = -27 The x term is -13x2. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x2 + 42.25 + x4 = -27 + 42.25 Reorder the terms: 42.25 + -13x2 + x4 = -27 + 42.25 Combine like terms: -27 + 42.25 = 15.25 42.25 + -13x2 + x4 = 15.25 Factor a perfect square on the left side: (x2 + -6.5)(x2 + -6.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x2 + -6.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x2 + -6.5 = 3.905124838 Simplifying x2 + -6.5 = 3.905124838 Reorder the terms: -6.5 + x2 = 3.905124838 Solving -6.5 + x2 = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x2 = 3.905124838 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x2 = 3.905124838 + 6.5 x2 = 3.905124838 + 6.5 Combine like terms: 3.905124838 + 6.5 = 10.405124838 x2 = 10.405124838 Simplifying x2 = 10.405124838 Take the square root of each side: x = {-3.225697574, 3.225697574}Subproblem 2
x2 + -6.5 = -3.905124838 Simplifying x2 + -6.5 = -3.905124838 Reorder the terms: -6.5 + x2 = -3.905124838 Solving -6.5 + x2 = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x2 = -3.905124838 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x2 = -3.905124838 + 6.5 x2 = -3.905124838 + 6.5 Combine like terms: -3.905124838 + 6.5 = 2.594875162 x2 = 2.594875162 Simplifying x2 = 2.594875162 Take the square root of each side: x = {-1.610861621, 1.610861621}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.225697574, 3.225697574, -1.610861621, 1.610861621}Solution
x = {0, -3.225697574, 3.225697574, -1.610861621, 1.610861621}
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