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Simplifying x3 + -24x2 + 112x = 0 Reorder the terms: 112x + -24x2 + x3 = 0 Solving 112x + -24x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(112 + -24x + 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 '(112 + -24x + x2)' equal to zero and attempt to solve: Simplifying 112 + -24x + x2 = 0 Solving 112 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-112' to each side of the equation. 112 + -24x + -112 + x2 = 0 + -112 Reorder the terms: 112 + -112 + -24x + x2 = 0 + -112 Combine like terms: 112 + -112 = 0 0 + -24x + x2 = 0 + -112 -24x + x2 = 0 + -112 Combine like terms: 0 + -112 = -112 -24x + x2 = -112 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -112 + 144 Reorder the terms: 144 + -24x + x2 = -112 + 144 Combine like terms: -112 + 144 = 32 144 + -24x + x2 = 32 Factor a perfect square on the left side: (x + -12)(x + -12) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + -12) equal to 5.656854249 and -5.656854249.Subproblem 1
x + -12 = 5.656854249 Simplifying x + -12 = 5.656854249 Reorder the terms: -12 + x = 5.656854249 Solving -12 + x = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 5.656854249 + 12 Combine like terms: -12 + 12 = 0 0 + x = 5.656854249 + 12 x = 5.656854249 + 12 Combine like terms: 5.656854249 + 12 = 17.656854249 x = 17.656854249 Simplifying x = 17.656854249Subproblem 2
x + -12 = -5.656854249 Simplifying x + -12 = -5.656854249 Reorder the terms: -12 + x = -5.656854249 Solving -12 + x = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -5.656854249 + 12 Combine like terms: -12 + 12 = 0 0 + x = -5.656854249 + 12 x = -5.656854249 + 12 Combine like terms: -5.656854249 + 12 = 6.343145751 x = 6.343145751 Simplifying x = 6.343145751Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.656854249, 6.343145751}Solution
x = {0, 17.656854249, 6.343145751}
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