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Simplifying x3 + -8x2 + x = 0 Reorder the terms: x + -8x2 + x3 = 0 Solving x + -8x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + -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 '(1 + -8x + x2)' equal to zero and attempt to solve: Simplifying 1 + -8x + x2 = 0 Solving 1 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -8x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -8x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8x + x2 = 0 + -1 -8x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -8x + x2 = -1 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 = -1 + 16 Reorder the terms: 16 + -8x + x2 = -1 + 16 Combine like terms: -1 + 16 = 15 16 + -8x + x2 = 15 Factor a perfect square on the left side: (x + -4)(x + -4) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -4) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -4 = 3.872983346 Simplifying x + -4 = 3.872983346 Reorder the terms: -4 + x = 3.872983346 Solving -4 + x = 3.872983346 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 = 3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.872983346 + 4 x = 3.872983346 + 4 Combine like terms: 3.872983346 + 4 = 7.872983346 x = 7.872983346 Simplifying x = 7.872983346Subproblem 2
x + -4 = -3.872983346 Simplifying x + -4 = -3.872983346 Reorder the terms: -4 + x = -3.872983346 Solving -4 + x = -3.872983346 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 = -3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.872983346 + 4 x = -3.872983346 + 4 Combine like terms: -3.872983346 + 4 = 0.127016654 x = 0.127016654 Simplifying x = 0.127016654Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.872983346, 0.127016654}Solution
x = {0, 7.872983346, 0.127016654}
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