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Simplifying x3 + -2x2 + -20x = 0 Reorder the terms: -20x + -2x2 + x3 = 0 Solving -20x + -2x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-20 + -2x + 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 + -2x + x2)' equal to zero and attempt to solve: Simplifying -20 + -2x + x2 = 0 Solving -20 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -2x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -2x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -2x + x2 = 0 + 20 -2x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -2x + x2 = 20 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 20 + 1 Reorder the terms: 1 + -2x + x2 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + -2x + x2 = 21 Factor a perfect square on the left side: (x + -1)(x + -1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + -1) equal to 4.582575695 and -4.582575695.Subproblem 1
x + -1 = 4.582575695 Simplifying x + -1 = 4.582575695 Reorder the terms: -1 + x = 4.582575695 Solving -1 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.582575695 + 1 x = 4.582575695 + 1 Combine like terms: 4.582575695 + 1 = 5.582575695 x = 5.582575695 Simplifying x = 5.582575695Subproblem 2
x + -1 = -4.582575695 Simplifying x + -1 = -4.582575695 Reorder the terms: -1 + x = -4.582575695 Solving -1 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.582575695 + 1 x = -4.582575695 + 1 Combine like terms: -4.582575695 + 1 = -3.582575695 x = -3.582575695 Simplifying x = -3.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.582575695, -3.582575695}Solution
x = {0, 5.582575695, -3.582575695}
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