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Simplifying x3 + -13x2 + 41x = 0 Reorder the terms: 41x + -13x2 + x3 = 0 Solving 41x + -13x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(41 + -13x + x2) = 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 '(41 + -13x + x2)' equal to zero and attempt to solve: Simplifying 41 + -13x + x2 = 0 Solving 41 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + -13x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + -13x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -13x + x2 = 0 + -41 -13x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 -13x + x2 = -41 The x term is -13x. 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. -13x + 42.25 + x2 = -41 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -41 + 42.25 Combine like terms: -41 + 42.25 = 1.25 42.25 + -13x + x2 = 1.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -6.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -6.5 = 1.118033989 Simplifying x + -6.5 = 1.118033989 Reorder the terms: -6.5 + x = 1.118033989 Solving -6.5 + x = 1.118033989 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 + x = 1.118033989 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 1.118033989 + 6.5 x = 1.118033989 + 6.5 Combine like terms: 1.118033989 + 6.5 = 7.618033989 x = 7.618033989 Simplifying x = 7.618033989Subproblem 2
x + -6.5 = -1.118033989 Simplifying x + -6.5 = -1.118033989 Reorder the terms: -6.5 + x = -1.118033989 Solving -6.5 + x = -1.118033989 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 + x = -1.118033989 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -1.118033989 + 6.5 x = -1.118033989 + 6.5 Combine like terms: -1.118033989 + 6.5 = 5.381966011 x = 5.381966011 Simplifying x = 5.381966011Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.618033989, 5.381966011}Solution
x = {0, 7.618033989, 5.381966011}
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