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Simplifying x3 + 23x2 + -2x = 0 Reorder the terms: -2x + 23x2 + x3 = 0 Solving -2x + 23x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-2 + 23x + 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 '(-2 + 23x + x2)' equal to zero and attempt to solve: Simplifying -2 + 23x + x2 = 0 Solving -2 + 23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 23x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 23x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 23x + x2 = 0 + 2 23x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 23x + x2 = 2 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = 2 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 2 + 132.25 Combine like terms: 2 + 132.25 = 134.25 132.25 + 23x + x2 = 134.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 134.25 Calculate the square root of the right side: 11.586630226 Break this problem into two subproblems by setting (x + 11.5) equal to 11.586630226 and -11.586630226.Subproblem 1
x + 11.5 = 11.586630226 Simplifying x + 11.5 = 11.586630226 Reorder the terms: 11.5 + x = 11.586630226 Solving 11.5 + x = 11.586630226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 11.586630226 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 11.586630226 + -11.5 x = 11.586630226 + -11.5 Combine like terms: 11.586630226 + -11.5 = 0.086630226 x = 0.086630226 Simplifying x = 0.086630226Subproblem 2
x + 11.5 = -11.586630226 Simplifying x + 11.5 = -11.586630226 Reorder the terms: 11.5 + x = -11.586630226 Solving 11.5 + x = -11.586630226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -11.586630226 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -11.586630226 + -11.5 x = -11.586630226 + -11.5 Combine like terms: -11.586630226 + -11.5 = -23.086630226 x = -23.086630226 Simplifying x = -23.086630226Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.086630226, -23.086630226}Solution
x = {0, 0.086630226, -23.086630226}
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