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Simplifying x3 + -3x2 + -13x = 0 Reorder the terms: -13x + -3x2 + x3 = 0 Solving -13x + -3x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-13 + -3x + 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 '(-13 + -3x + x2)' equal to zero and attempt to solve: Simplifying -13 + -3x + x2 = 0 Solving -13 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -3x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -3x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -3x + x2 = 0 + 13 -3x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -3x + x2 = 13 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 13 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 13 + 2.25 Combine like terms: 13 + 2.25 = 15.25 2.25 + -3x + x2 = 15.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + -1.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + -1.5 = 3.905124838 Simplifying x + -1.5 = 3.905124838 Reorder the terms: -1.5 + x = 3.905124838 Solving -1.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.905124838 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.905124838 + 1.5 x = 3.905124838 + 1.5 Combine like terms: 3.905124838 + 1.5 = 5.405124838 x = 5.405124838 Simplifying x = 5.405124838Subproblem 2
x + -1.5 = -3.905124838 Simplifying x + -1.5 = -3.905124838 Reorder the terms: -1.5 + x = -3.905124838 Solving -1.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.905124838 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.905124838 + 1.5 x = -3.905124838 + 1.5 Combine like terms: -3.905124838 + 1.5 = -2.405124838 x = -2.405124838 Simplifying x = -2.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.405124838, -2.405124838}Solution
x = {0, 5.405124838, -2.405124838}
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