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Simplifying x3 + 7x2 + 5x = 0 Reorder the terms: 5x + 7x2 + x3 = 0 Solving 5x + 7x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 7x + 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 '(5 + 7x + x2)' equal to zero and attempt to solve: Simplifying 5 + 7x + x2 = 0 Solving 5 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 7x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 7x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7x + x2 = 0 + -5 7x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 7x + x2 = -5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -5 + 12.25 Combine like terms: -5 + 12.25 = 7.25 12.25 + 7x + x2 = 7.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + 3.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + 3.5 = 2.692582404 Simplifying x + 3.5 = 2.692582404 Reorder the terms: 3.5 + x = 2.692582404 Solving 3.5 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 2.692582404 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.692582404 + -3.5 x = 2.692582404 + -3.5 Combine like terms: 2.692582404 + -3.5 = -0.807417596 x = -0.807417596 Simplifying x = -0.807417596Subproblem 2
x + 3.5 = -2.692582404 Simplifying x + 3.5 = -2.692582404 Reorder the terms: 3.5 + x = -2.692582404 Solving 3.5 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -2.692582404 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.692582404 + -3.5 x = -2.692582404 + -3.5 Combine like terms: -2.692582404 + -3.5 = -6.192582404 x = -6.192582404 Simplifying x = -6.192582404Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.807417596, -6.192582404}Solution
x = {0, -0.807417596, -6.192582404}
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