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Simplifying x3 + -4x2 + -44x = 0 Reorder the terms: -44x + -4x2 + x3 = 0 Solving -44x + -4x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-44 + -4x + 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 '(-44 + -4x + x2)' equal to zero and attempt to solve: Simplifying -44 + -4x + x2 = 0 Solving -44 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -4x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + -4x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -4x + x2 = 0 + 44 -4x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 -4x + x2 = 44 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 44 + 4 Reorder the terms: 4 + -4x + x2 = 44 + 4 Combine like terms: 44 + 4 = 48 4 + -4x + x2 = 48 Factor a perfect square on the left side: (x + -2)(x + -2) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + -2) equal to 6.92820323 and -6.92820323.Subproblem 1
x + -2 = 6.92820323 Simplifying x + -2 = 6.92820323 Reorder the terms: -2 + x = 6.92820323 Solving -2 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 6.92820323 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6.92820323 + 2 x = 6.92820323 + 2 Combine like terms: 6.92820323 + 2 = 8.92820323 x = 8.92820323 Simplifying x = 8.92820323Subproblem 2
x + -2 = -6.92820323 Simplifying x + -2 = -6.92820323 Reorder the terms: -2 + x = -6.92820323 Solving -2 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -6.92820323 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6.92820323 + 2 x = -6.92820323 + 2 Combine like terms: -6.92820323 + 2 = -4.92820323 x = -4.92820323 Simplifying x = -4.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.92820323, -4.92820323}Solution
x = {0, 8.92820323, -4.92820323}
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