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Simplifying x4 + 8x3 + 8x2 = 0 Reorder the terms: 8x2 + 8x3 + x4 = 0 Solving 8x2 + 8x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(8 + 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 '(8 + 8x + x2)' equal to zero and attempt to solve: Simplifying 8 + 8x + x2 = 0 Solving 8 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 8x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 8x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 8x + x2 = 0 + -8 8x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 8x + x2 = -8 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 = -8 + 16 Reorder the terms: 16 + 8x + x2 = -8 + 16 Combine like terms: -8 + 16 = 8 16 + 8x + x2 = 8 Factor a perfect square on the left side: (x + 4)(x + 4) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + 4) equal to 2.828427125 and -2.828427125.Subproblem 1
x + 4 = 2.828427125 Simplifying x + 4 = 2.828427125 Reorder the terms: 4 + x = 2.828427125 Solving 4 + x = 2.828427125 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 = 2.828427125 + -4 Combine like terms: 4 + -4 = 0 0 + x = 2.828427125 + -4 x = 2.828427125 + -4 Combine like terms: 2.828427125 + -4 = -1.171572875 x = -1.171572875 Simplifying x = -1.171572875Subproblem 2
x + 4 = -2.828427125 Simplifying x + 4 = -2.828427125 Reorder the terms: 4 + x = -2.828427125 Solving 4 + x = -2.828427125 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 = -2.828427125 + -4 Combine like terms: 4 + -4 = 0 0 + x = -2.828427125 + -4 x = -2.828427125 + -4 Combine like terms: -2.828427125 + -4 = -6.828427125 x = -6.828427125 Simplifying x = -6.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.171572875, -6.828427125}Solution
x = {0, -1.171572875, -6.828427125}
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