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Simplifying x3 + 8x2 + -16x = 0 Reorder the terms: -16x + 8x2 + x3 = 0 Solving -16x + 8x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-16 + 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 '(-16 + 8x + x2)' equal to zero and attempt to solve: Simplifying -16 + 8x + x2 = 0 Solving -16 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 8x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 8x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 8x + x2 = 0 + 16 8x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 8x + x2 = 16 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 = 16 + 16 Reorder the terms: 16 + 8x + x2 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + 8x + x2 = 32 Factor a perfect square on the left side: (x + 4)(x + 4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 4) equal to 5.656854249 and -5.656854249.Subproblem 1
x + 4 = 5.656854249 Simplifying x + 4 = 5.656854249 Reorder the terms: 4 + x = 5.656854249 Solving 4 + x = 5.656854249 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 = 5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.656854249 + -4 x = 5.656854249 + -4 Combine like terms: 5.656854249 + -4 = 1.656854249 x = 1.656854249 Simplifying x = 1.656854249Subproblem 2
x + 4 = -5.656854249 Simplifying x + 4 = -5.656854249 Reorder the terms: 4 + x = -5.656854249 Solving 4 + x = -5.656854249 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 = -5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.656854249 + -4 x = -5.656854249 + -4 Combine like terms: -5.656854249 + -4 = -9.656854249 x = -9.656854249 Simplifying x = -9.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.656854249, -9.656854249}Solution
x = {0, 1.656854249, -9.656854249}
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