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Simplifying 5x3 + 55x2 + 10x = 0 Reorder the terms: 10x + 55x2 + 5x3 = 0 Solving 10x + 55x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(2 + 11x + x2) = 0 Ignore the factor 5.Subproblem 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 '(2 + 11x + x2)' equal to zero and attempt to solve: Simplifying 2 + 11x + x2 = 0 Solving 2 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 11x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 11x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 11x + x2 = 0 + -2 11x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 11x + x2 = -2 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = -2 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -2 + 30.25 Combine like terms: -2 + 30.25 = 28.25 30.25 + 11x + x2 = 28.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + 5.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + 5.5 = 5.315072906 Simplifying x + 5.5 = 5.315072906 Reorder the terms: 5.5 + x = 5.315072906 Solving 5.5 + x = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 5.315072906 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 5.315072906 + -5.5 x = 5.315072906 + -5.5 Combine like terms: 5.315072906 + -5.5 = -0.184927094 x = -0.184927094 Simplifying x = -0.184927094Subproblem 2
x + 5.5 = -5.315072906 Simplifying x + 5.5 = -5.315072906 Reorder the terms: 5.5 + x = -5.315072906 Solving 5.5 + x = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -5.315072906 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -5.315072906 + -5.5 x = -5.315072906 + -5.5 Combine like terms: -5.315072906 + -5.5 = -10.815072906 x = -10.815072906 Simplifying x = -10.815072906Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.184927094, -10.815072906}Solution
x = {0, -0.184927094, -10.815072906}
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