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Simplifying x3 + -8x2 + -24x = 0 Reorder the terms: -24x + -8x2 + x3 = 0 Solving -24x + -8x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-24 + -8x + 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 '(-24 + -8x + x2)' equal to zero and attempt to solve: Simplifying -24 + -8x + x2 = 0 Solving -24 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -8x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -8x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -8x + x2 = 0 + 24 -8x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -8x + x2 = 24 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 24 + 16 Reorder the terms: 16 + -8x + x2 = 24 + 16 Combine like terms: 24 + 16 = 40 16 + -8x + x2 = 40 Factor a perfect square on the left side: (x + -4)(x + -4) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + -4) equal to 6.32455532 and -6.32455532.Subproblem 1
x + -4 = 6.32455532 Simplifying x + -4 = 6.32455532 Reorder the terms: -4 + x = 6.32455532 Solving -4 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 6.32455532 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.32455532 + 4 x = 6.32455532 + 4 Combine like terms: 6.32455532 + 4 = 10.32455532 x = 10.32455532 Simplifying x = 10.32455532Subproblem 2
x + -4 = -6.32455532 Simplifying x + -4 = -6.32455532 Reorder the terms: -4 + x = -6.32455532 Solving -4 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -6.32455532 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.32455532 + 4 x = -6.32455532 + 4 Combine like terms: -6.32455532 + 4 = -2.32455532 x = -2.32455532 Simplifying x = -2.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.32455532, -2.32455532}Solution
x = {0, 10.32455532, -2.32455532}
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