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Simplifying x3 + 8x2 + -23x = 0 Reorder the terms: -23x + 8x2 + x3 = 0 Solving -23x + 8x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-23 + 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 '(-23 + 8x + x2)' equal to zero and attempt to solve: Simplifying -23 + 8x + x2 = 0 Solving -23 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 8x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 8x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 8x + x2 = 0 + 23 8x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 8x + x2 = 23 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 = 23 + 16 Reorder the terms: 16 + 8x + x2 = 23 + 16 Combine like terms: 23 + 16 = 39 16 + 8x + x2 = 39 Factor a perfect square on the left side: (x + 4)(x + 4) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + 4) equal to 6.244997998 and -6.244997998.Subproblem 1
x + 4 = 6.244997998 Simplifying x + 4 = 6.244997998 Reorder the terms: 4 + x = 6.244997998 Solving 4 + x = 6.244997998 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 = 6.244997998 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.244997998 + -4 x = 6.244997998 + -4 Combine like terms: 6.244997998 + -4 = 2.244997998 x = 2.244997998 Simplifying x = 2.244997998Subproblem 2
x + 4 = -6.244997998 Simplifying x + 4 = -6.244997998 Reorder the terms: 4 + x = -6.244997998 Solving 4 + x = -6.244997998 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 = -6.244997998 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.244997998 + -4 x = -6.244997998 + -4 Combine like terms: -6.244997998 + -4 = -10.244997998 x = -10.244997998 Simplifying x = -10.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.244997998, -10.244997998}Solution
x = {0, 2.244997998, -10.244997998}
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