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Simplifying x3 + x2 + -8x = 0 Reorder the terms: -8x + x2 + x3 = 0 Solving -8x + x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + x + 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 '(-8 + x + x2)' equal to zero and attempt to solve: Simplifying -8 + x + x2 = 0 Solving -8 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x + x2 = 0 + 8 x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 x + x2 = 8 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 8 + 0.25 Reorder the terms: 0.25 + x + x2 = 8 + 0.25 Combine like terms: 8 + 0.25 = 8.25 0.25 + x + x2 = 8.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + 0.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + 0.5 = 2.872281323 Simplifying x + 0.5 = 2.872281323 Reorder the terms: 0.5 + x = 2.872281323 Solving 0.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.872281323 + -0.5 x = 2.872281323 + -0.5 Combine like terms: 2.872281323 + -0.5 = 2.372281323 x = 2.372281323 Simplifying x = 2.372281323Subproblem 2
x + 0.5 = -2.872281323 Simplifying x + 0.5 = -2.872281323 Reorder the terms: 0.5 + x = -2.872281323 Solving 0.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.872281323 + -0.5 x = -2.872281323 + -0.5 Combine like terms: -2.872281323 + -0.5 = -3.372281323 x = -3.372281323 Simplifying x = -3.372281323Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.372281323, -3.372281323}Solution
x = {0, 2.372281323, -3.372281323}
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