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Simplifying x3 + -9x2 + -20x = 0 Reorder the terms: -20x + -9x2 + x3 = 0 Solving -20x + -9x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-20 + -9x + 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 '(-20 + -9x + x2)' equal to zero and attempt to solve: Simplifying -20 + -9x + x2 = 0 Solving -20 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -9x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -9x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -9x + x2 = 0 + 20 -9x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -9x + x2 = 20 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 20 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 20 + 20.25 Combine like terms: 20 + 20.25 = 40.25 20.25 + -9x + x2 = 40.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + -4.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + -4.5 = 6.34428877 Simplifying x + -4.5 = 6.34428877 Reorder the terms: -4.5 + x = 6.34428877 Solving -4.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 6.34428877 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6.34428877 + 4.5 x = 6.34428877 + 4.5 Combine like terms: 6.34428877 + 4.5 = 10.84428877 x = 10.84428877 Simplifying x = 10.84428877Subproblem 2
x + -4.5 = -6.34428877 Simplifying x + -4.5 = -6.34428877 Reorder the terms: -4.5 + x = -6.34428877 Solving -4.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -6.34428877 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6.34428877 + 4.5 x = -6.34428877 + 4.5 Combine like terms: -6.34428877 + 4.5 = -1.84428877 x = -1.84428877 Simplifying x = -1.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.84428877, -1.84428877}Solution
x = {0, 10.84428877, -1.84428877}
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