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Simplifying X3 + -4X2 + 5X + -20X = 0 Reorder the terms: 5X + -20X + -4X2 + X3 = 0 Combine like terms: 5X + -20X = -15X -15X + -4X2 + X3 = 0 Solving -15X + -4X2 + X3 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), 'X'. X(-15 + -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 '(-15 + -4X + X2)' equal to zero and attempt to solve: Simplifying -15 + -4X + X2 = 0 Solving -15 + -4X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -4X + 15 + X2 = 0 + 15 Reorder the terms: -15 + 15 + -4X + X2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4X + X2 = 0 + 15 -4X + X2 = 0 + 15 Combine like terms: 0 + 15 = 15 -4X + X2 = 15 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 = 15 + 4 Reorder the terms: 4 + -4X + X2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + -4X + X2 = 19 Factor a perfect square on the left side: (X + -2)(X + -2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (X + -2) equal to 4.358898944 and -4.358898944.Subproblem 1
X + -2 = 4.358898944 Simplifying X + -2 = 4.358898944 Reorder the terms: -2 + X = 4.358898944 Solving -2 + X = 4.358898944 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 = 4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + X = 4.358898944 + 2 X = 4.358898944 + 2 Combine like terms: 4.358898944 + 2 = 6.358898944 X = 6.358898944 Simplifying X = 6.358898944Subproblem 2
X + -2 = -4.358898944 Simplifying X + -2 = -4.358898944 Reorder the terms: -2 + X = -4.358898944 Solving -2 + X = -4.358898944 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 = -4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + X = -4.358898944 + 2 X = -4.358898944 + 2 Combine like terms: -4.358898944 + 2 = -2.358898944 X = -2.358898944 Simplifying X = -2.358898944Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.358898944, -2.358898944}Solution
X = {0, 6.358898944, -2.358898944}
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