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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 = 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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