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Simplifying x3 + -11x2 + -3x = 0 Reorder the terms: -3x + -11x2 + x3 = 0 Solving -3x + -11x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + -11x + 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 '(-3 + -11x + x2)' equal to zero and attempt to solve: Simplifying -3 + -11x + x2 = 0 Solving -3 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -11x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -11x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -11x + x2 = 0 + 3 -11x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -11x + x2 = 3 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 3 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 3 + 30.25 Combine like terms: 3 + 30.25 = 33.25 30.25 + -11x + x2 = 33.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + -5.5) equal to 5.766281297 and -5.766281297.Subproblem 1
x + -5.5 = 5.766281297 Simplifying x + -5.5 = 5.766281297 Reorder the terms: -5.5 + x = 5.766281297 Solving -5.5 + x = 5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.766281297 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.766281297 + 5.5 x = 5.766281297 + 5.5 Combine like terms: 5.766281297 + 5.5 = 11.266281297 x = 11.266281297 Simplifying x = 11.266281297Subproblem 2
x + -5.5 = -5.766281297 Simplifying x + -5.5 = -5.766281297 Reorder the terms: -5.5 + x = -5.766281297 Solving -5.5 + x = -5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.766281297 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.766281297 + 5.5 x = -5.766281297 + 5.5 Combine like terms: -5.766281297 + 5.5 = -0.266281297 x = -0.266281297 Simplifying x = -0.266281297Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.266281297, -0.266281297}Solution
x = {0, 11.266281297, -0.266281297}
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