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Simplifying x3 + 8x2 + -4x = 0 Reorder the terms: -4x + 8x2 + x3 = 0 Solving -4x + 8x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + 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 '(-4 + 8x + x2)' equal to zero and attempt to solve: Simplifying -4 + 8x + x2 = 0 Solving -4 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 8x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 8x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 8x + x2 = 0 + 4 8x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 8x + x2 = 4 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 = 4 + 16 Reorder the terms: 16 + 8x + x2 = 4 + 16 Combine like terms: 4 + 16 = 20 16 + 8x + x2 = 20 Factor a perfect square on the left side: (x + 4)(x + 4) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 4) equal to 4.472135955 and -4.472135955.Subproblem 1
x + 4 = 4.472135955 Simplifying x + 4 = 4.472135955 Reorder the terms: 4 + x = 4.472135955 Solving 4 + x = 4.472135955 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 = 4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.472135955 + -4 x = 4.472135955 + -4 Combine like terms: 4.472135955 + -4 = 0.472135955 x = 0.472135955 Simplifying x = 0.472135955Subproblem 2
x + 4 = -4.472135955 Simplifying x + 4 = -4.472135955 Reorder the terms: 4 + x = -4.472135955 Solving 4 + x = -4.472135955 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 = -4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.472135955 + -4 x = -4.472135955 + -4 Combine like terms: -4.472135955 + -4 = -8.472135955 x = -8.472135955 Simplifying x = -8.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.472135955, -8.472135955}Solution
x = {0, 0.472135955, -8.472135955}
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