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Simplifying x3 + -200x2 + 2x = 0 Reorder the terms: 2x + -200x2 + x3 = 0 Solving 2x + -200x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(2 + -200x + 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 '(2 + -200x + x2)' equal to zero and attempt to solve: Simplifying 2 + -200x + x2 = 0 Solving 2 + -200x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -200x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -200x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -200x + x2 = 0 + -2 -200x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -200x + x2 = -2 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -2 + 10000 Reorder the terms: 10000 + -200x + x2 = -2 + 10000 Combine like terms: -2 + 10000 = 9998 10000 + -200x + x2 = 9998 Factor a perfect square on the left side: (x + -100)(x + -100) = 9998 Calculate the square root of the right side: 99.9899995 Break this problem into two subproblems by setting (x + -100) equal to 99.9899995 and -99.9899995.Subproblem 1
x + -100 = 99.9899995 Simplifying x + -100 = 99.9899995 Reorder the terms: -100 + x = 99.9899995 Solving -100 + x = 99.9899995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 99.9899995 + 100 Combine like terms: -100 + 100 = 0 0 + x = 99.9899995 + 100 x = 99.9899995 + 100 Combine like terms: 99.9899995 + 100 = 199.9899995 x = 199.9899995 Simplifying x = 199.9899995Subproblem 2
x + -100 = -99.9899995 Simplifying x + -100 = -99.9899995 Reorder the terms: -100 + x = -99.9899995 Solving -100 + x = -99.9899995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -99.9899995 + 100 Combine like terms: -100 + 100 = 0 0 + x = -99.9899995 + 100 x = -99.9899995 + 100 Combine like terms: -99.9899995 + 100 = 0.0100005 x = 0.0100005 Simplifying x = 0.0100005Solution
The solution to the problem is based on the solutions from the subproblems. x = {199.9899995, 0.0100005}Solution
x = {0, 199.9899995, 0.0100005}
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