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Simplifying x3 + -5x2 + -8x = 0 Reorder the terms: -8x + -5x2 + x3 = 0 Solving -8x + -5x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + -5x + 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 + -5x + x2)' equal to zero and attempt to solve: Simplifying -8 + -5x + x2 = 0 Solving -8 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5x + x2 = 0 + 8 -5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -5x + x2 = 8 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 8 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 8 + 6.25 Combine like terms: 8 + 6.25 = 14.25 6.25 + -5x + x2 = 14.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + -2.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + -2.5 = 3.774917218 Simplifying x + -2.5 = 3.774917218 Reorder the terms: -2.5 + x = 3.774917218 Solving -2.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.774917218 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.774917218 + 2.5 x = 3.774917218 + 2.5 Combine like terms: 3.774917218 + 2.5 = 6.274917218 x = 6.274917218 Simplifying x = 6.274917218Subproblem 2
x + -2.5 = -3.774917218 Simplifying x + -2.5 = -3.774917218 Reorder the terms: -2.5 + x = -3.774917218 Solving -2.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.774917218 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.774917218 + 2.5 x = -3.774917218 + 2.5 Combine like terms: -3.774917218 + 2.5 = -1.274917218 x = -1.274917218 Simplifying x = -1.274917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.274917218, -1.274917218}Solution
x = {0, 6.274917218, -1.274917218}
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