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Simplifying x3 + -12x2 + -6x = 0 Reorder the terms: -6x + -12x2 + x3 = 0 Solving -6x + -12x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + -12x + 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 '(-6 + -12x + x2)' equal to zero and attempt to solve: Simplifying -6 + -12x + x2 = 0 Solving -6 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -12x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -12x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -12x + x2 = 0 + 6 -12x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -12x + x2 = 6 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 6 + 36 Reorder the terms: 36 + -12x + x2 = 6 + 36 Combine like terms: 6 + 36 = 42 36 + -12x + x2 = 42 Factor a perfect square on the left side: (x + -6)(x + -6) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (x + -6) equal to 6.480740698 and -6.480740698.Subproblem 1
x + -6 = 6.480740698 Simplifying x + -6 = 6.480740698 Reorder the terms: -6 + x = 6.480740698 Solving -6 + x = 6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 6.480740698 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.480740698 + 6 x = 6.480740698 + 6 Combine like terms: 6.480740698 + 6 = 12.480740698 x = 12.480740698 Simplifying x = 12.480740698Subproblem 2
x + -6 = -6.480740698 Simplifying x + -6 = -6.480740698 Reorder the terms: -6 + x = -6.480740698 Solving -6 + x = -6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -6.480740698 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.480740698 + 6 x = -6.480740698 + 6 Combine like terms: -6.480740698 + 6 = -0.480740698 x = -0.480740698 Simplifying x = -0.480740698Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.480740698, -0.480740698}Solution
x = {0, 12.480740698, -0.480740698}
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