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Simplifying X3 + -20X2 + 25X = 0 Reorder the terms: 25X + -20X2 + X3 = 0 Solving 25X + -20X2 + X3 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), 'X'. X(25 + -20X + 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 '(25 + -20X + X2)' equal to zero and attempt to solve: Simplifying 25 + -20X + X2 = 0 Solving 25 + -20X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -20X + -25 + X2 = 0 + -25 Reorder the terms: 25 + -25 + -20X + X2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -20X + X2 = 0 + -25 -20X + X2 = 0 + -25 Combine like terms: 0 + -25 = -25 -20X + X2 = -25 The X term is -20X. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20X + 100 + X2 = -25 + 100 Reorder the terms: 100 + -20X + X2 = -25 + 100 Combine like terms: -25 + 100 = 75 100 + -20X + X2 = 75 Factor a perfect square on the left side: (X + -10)(X + -10) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (X + -10) equal to 8.660254038 and -8.660254038.Subproblem 1
X + -10 = 8.660254038 Simplifying X + -10 = 8.660254038 Reorder the terms: -10 + X = 8.660254038 Solving -10 + X = 8.660254038 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + X = 8.660254038 + 10 Combine like terms: -10 + 10 = 0 0 + X = 8.660254038 + 10 X = 8.660254038 + 10 Combine like terms: 8.660254038 + 10 = 18.660254038 X = 18.660254038 Simplifying X = 18.660254038Subproblem 2
X + -10 = -8.660254038 Simplifying X + -10 = -8.660254038 Reorder the terms: -10 + X = -8.660254038 Solving -10 + X = -8.660254038 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + X = -8.660254038 + 10 Combine like terms: -10 + 10 = 0 0 + X = -8.660254038 + 10 X = -8.660254038 + 10 Combine like terms: -8.660254038 + 10 = 1.339745962 X = 1.339745962 Simplifying X = 1.339745962Solution
The solution to the problem is based on the solutions from the subproblems. X = {18.660254038, 1.339745962}Solution
X = {0, 18.660254038, 1.339745962}
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