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Simplifying x3 + 6x2 + -11x = 0 Reorder the terms: -11x + 6x2 + x3 = 0 Solving -11x + 6x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + 6x + 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 '(-11 + 6x + x2)' equal to zero and attempt to solve: Simplifying -11 + 6x + x2 = 0 Solving -11 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 6x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 6x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 6x + x2 = 0 + 11 6x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 6x + x2 = 11 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 11 + 9 Reorder the terms: 9 + 6x + x2 = 11 + 9 Combine like terms: 11 + 9 = 20 9 + 6x + x2 = 20 Factor a perfect square on the left side: (x + 3)(x + 3) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 3) equal to 4.472135955 and -4.472135955.Subproblem 1
x + 3 = 4.472135955 Simplifying x + 3 = 4.472135955 Reorder the terms: 3 + x = 4.472135955 Solving 3 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.472135955 + -3 x = 4.472135955 + -3 Combine like terms: 4.472135955 + -3 = 1.472135955 x = 1.472135955 Simplifying x = 1.472135955Subproblem 2
x + 3 = -4.472135955 Simplifying x + 3 = -4.472135955 Reorder the terms: 3 + x = -4.472135955 Solving 3 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.472135955 + -3 x = -4.472135955 + -3 Combine like terms: -4.472135955 + -3 = -7.472135955 x = -7.472135955 Simplifying x = -7.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.472135955, -7.472135955}Solution
x = {0, 1.472135955, -7.472135955}
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