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Simplifying x3 + -5x2 + -17x = 0 Reorder the terms: -17x + -5x2 + x3 = 0 Solving -17x + -5x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-17 + -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 '(-17 + -5x + x2)' equal to zero and attempt to solve: Simplifying -17 + -5x + x2 = 0 Solving -17 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -5x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -5x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -5x + x2 = 0 + 17 -5x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -5x + x2 = 17 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 = 17 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 17 + 6.25 Combine like terms: 17 + 6.25 = 23.25 6.25 + -5x + x2 = 23.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (x + -2.5) equal to 4.82182538 and -4.82182538.Subproblem 1
x + -2.5 = 4.82182538 Simplifying x + -2.5 = 4.82182538 Reorder the terms: -2.5 + x = 4.82182538 Solving -2.5 + x = 4.82182538 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 = 4.82182538 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.82182538 + 2.5 x = 4.82182538 + 2.5 Combine like terms: 4.82182538 + 2.5 = 7.32182538 x = 7.32182538 Simplifying x = 7.32182538Subproblem 2
x + -2.5 = -4.82182538 Simplifying x + -2.5 = -4.82182538 Reorder the terms: -2.5 + x = -4.82182538 Solving -2.5 + x = -4.82182538 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 = -4.82182538 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.82182538 + 2.5 x = -4.82182538 + 2.5 Combine like terms: -4.82182538 + 2.5 = -2.32182538 x = -2.32182538 Simplifying x = -2.32182538Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.32182538, -2.32182538}Solution
x = {0, 7.32182538, -2.32182538}
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