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Simplifying x3 + -11x2 + -20x = 0 Reorder the terms: -20x + -11x2 + x3 = 0 Solving -20x + -11x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-20 + -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 '(-20 + -11x + x2)' equal to zero and attempt to solve: Simplifying -20 + -11x + x2 = 0 Solving -20 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -11x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -11x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -11x + x2 = 0 + 20 -11x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -11x + x2 = 20 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 = 20 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 20 + 30.25 Combine like terms: 20 + 30.25 = 50.25 30.25 + -11x + x2 = 50.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x + -5.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x + -5.5 = 7.088723439 Simplifying x + -5.5 = 7.088723439 Reorder the terms: -5.5 + x = 7.088723439 Solving -5.5 + x = 7.088723439 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 = 7.088723439 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 7.088723439 + 5.5 x = 7.088723439 + 5.5 Combine like terms: 7.088723439 + 5.5 = 12.588723439 x = 12.588723439 Simplifying x = 12.588723439Subproblem 2
x + -5.5 = -7.088723439 Simplifying x + -5.5 = -7.088723439 Reorder the terms: -5.5 + x = -7.088723439 Solving -5.5 + x = -7.088723439 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 = -7.088723439 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -7.088723439 + 5.5 x = -7.088723439 + 5.5 Combine like terms: -7.088723439 + 5.5 = -1.588723439 x = -1.588723439 Simplifying x = -1.588723439Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.588723439, -1.588723439}Solution
x = {0, 12.588723439, -1.588723439}
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