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Simplifying x3 + -16x2 + 8x = 0 Reorder the terms: 8x + -16x2 + x3 = 0 Solving 8x + -16x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(8 + -16x + 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 + -16x + x2)' equal to zero and attempt to solve: Simplifying 8 + -16x + x2 = 0 Solving 8 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -16x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -16x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -16x + x2 = 0 + -8 -16x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -16x + x2 = -8 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -8 + 64 Reorder the terms: 64 + -16x + x2 = -8 + 64 Combine like terms: -8 + 64 = 56 64 + -16x + x2 = 56 Factor a perfect square on the left side: (x + -8)(x + -8) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + -8) equal to 7.483314774 and -7.483314774.Subproblem 1
x + -8 = 7.483314774 Simplifying x + -8 = 7.483314774 Reorder the terms: -8 + x = 7.483314774 Solving -8 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.483314774 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.483314774 + 8 x = 7.483314774 + 8 Combine like terms: 7.483314774 + 8 = 15.483314774 x = 15.483314774 Simplifying x = 15.483314774Subproblem 2
x + -8 = -7.483314774 Simplifying x + -8 = -7.483314774 Reorder the terms: -8 + x = -7.483314774 Solving -8 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.483314774 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.483314774 + 8 x = -7.483314774 + 8 Combine like terms: -7.483314774 + 8 = 0.516685226 x = 0.516685226 Simplifying x = 0.516685226Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.483314774, 0.516685226}Solution
x = {0, 15.483314774, 0.516685226}
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