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Simplifying x4 + -8x3 + -16x2 = 0 Reorder the terms: -16x2 + -8x3 + x4 = 0 Solving -16x2 + -8x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-16 + -8x + x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 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 = 9.656854249 x = 9.656854249 Simplifying x = 9.656854249Subproblem 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 = -1.656854249 x = -1.656854249 Simplifying x = -1.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.656854249, -1.656854249}Solution
x = {0, 9.656854249, -1.656854249}
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