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Simplifying x3 + -100x2 + 250x = 0 Reorder the terms: 250x + -100x2 + x3 = 0 Solving 250x + -100x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(250 + -100x + 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 '(250 + -100x + x2)' equal to zero and attempt to solve: Simplifying 250 + -100x + x2 = 0 Solving 250 + -100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-250' to each side of the equation. 250 + -100x + -250 + x2 = 0 + -250 Reorder the terms: 250 + -250 + -100x + x2 = 0 + -250 Combine like terms: 250 + -250 = 0 0 + -100x + x2 = 0 + -250 -100x + x2 = 0 + -250 Combine like terms: 0 + -250 = -250 -100x + x2 = -250 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -250 + 2500 Reorder the terms: 2500 + -100x + x2 = -250 + 2500 Combine like terms: -250 + 2500 = 2250 2500 + -100x + x2 = 2250 Factor a perfect square on the left side: (x + -50)(x + -50) = 2250 Calculate the square root of the right side: 47.434164903 Break this problem into two subproblems by setting (x + -50) equal to 47.434164903 and -47.434164903.Subproblem 1
x + -50 = 47.434164903 Simplifying x + -50 = 47.434164903 Reorder the terms: -50 + x = 47.434164903 Solving -50 + x = 47.434164903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 47.434164903 + 50 Combine like terms: -50 + 50 = 0 0 + x = 47.434164903 + 50 x = 47.434164903 + 50 Combine like terms: 47.434164903 + 50 = 97.434164903 x = 97.434164903 Simplifying x = 97.434164903Subproblem 2
x + -50 = -47.434164903 Simplifying x + -50 = -47.434164903 Reorder the terms: -50 + x = -47.434164903 Solving -50 + x = -47.434164903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -47.434164903 + 50 Combine like terms: -50 + 50 = 0 0 + x = -47.434164903 + 50 x = -47.434164903 + 50 Combine like terms: -47.434164903 + 50 = 2.565835097 x = 2.565835097 Simplifying x = 2.565835097Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.434164903, 2.565835097}Solution
x = {0, 97.434164903, 2.565835097}
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