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Simplifying 6x3 + -11x2 + -36x = 0 Reorder the terms: -36x + -11x2 + 6x3 = 0 Solving -36x + -11x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-36 + -11x + 6x2) = 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 '(-36 + -11x + 6x2)' equal to zero and attempt to solve: Simplifying -36 + -11x + 6x2 = 0 Solving -36 + -11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -6 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -1.833333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -1.833333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1.833333333x + x2 = 0 + 6 -1.833333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1.833333333x + x2 = 6 The x term is -1.833333333x. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333x + 0.8402777775 + x2 = 6 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 6 + 0.8402777775 Combine like terms: 6 + 0.8402777775 = 6.8402777775 0.8402777775 + -1.833333333x + x2 = 6.8402777775 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 6.8402777775 Calculate the square root of the right side: 2.615392471 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 2.615392471 and -2.615392471.Subproblem 1
x + -0.9166666665 = 2.615392471 Simplifying x + -0.9166666665 = 2.615392471 Reorder the terms: -0.9166666665 + x = 2.615392471 Solving -0.9166666665 + x = 2.615392471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = 2.615392471 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 2.615392471 + 0.9166666665 x = 2.615392471 + 0.9166666665 Combine like terms: 2.615392471 + 0.9166666665 = 3.5320591375 x = 3.5320591375 Simplifying x = 3.5320591375Subproblem 2
x + -0.9166666665 = -2.615392471 Simplifying x + -0.9166666665 = -2.615392471 Reorder the terms: -0.9166666665 + x = -2.615392471 Solving -0.9166666665 + x = -2.615392471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = -2.615392471 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -2.615392471 + 0.9166666665 x = -2.615392471 + 0.9166666665 Combine like terms: -2.615392471 + 0.9166666665 = -1.6987258045 x = -1.6987258045 Simplifying x = -1.6987258045Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5320591375, -1.6987258045}Solution
x = {0, 3.5320591375, -1.6987258045}
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