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Simplifying x3 + 5x2 + -1x = 0 Reorder the terms: -1x + 5x2 + x3 = 0 Solving -1x + 5x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + 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 '(-1 + 5x + x2)' equal to zero and attempt to solve: Simplifying -1 + 5x + x2 = 0 Solving -1 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5x + x2 = 0 + 1 5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 5x + x2 = 1 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 = 1 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1 + 6.25 Combine like terms: 1 + 6.25 = 7.25 6.25 + 5x + x2 = 7.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + 2.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + 2.5 = 2.692582404 Simplifying x + 2.5 = 2.692582404 Reorder the terms: 2.5 + x = 2.692582404 Solving 2.5 + x = 2.692582404 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 = 2.692582404 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.692582404 + -2.5 x = 2.692582404 + -2.5 Combine like terms: 2.692582404 + -2.5 = 0.192582404 x = 0.192582404 Simplifying x = 0.192582404Subproblem 2
x + 2.5 = -2.692582404 Simplifying x + 2.5 = -2.692582404 Reorder the terms: 2.5 + x = -2.692582404 Solving 2.5 + x = -2.692582404 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 = -2.692582404 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.692582404 + -2.5 x = -2.692582404 + -2.5 Combine like terms: -2.692582404 + -2.5 = -5.192582404 x = -5.192582404 Simplifying x = -5.192582404Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.192582404, -5.192582404}Solution
x = {0, 0.192582404, -5.192582404}
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