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Simplifying 5x(x + -2000) + -1x + 2000 = 0 Reorder the terms: 5x(-2000 + x) + -1x + 2000 = 0 (-2000 * 5x + x * 5x) + -1x + 2000 = 0 (-10000x + 5x2) + -1x + 2000 = 0 Reorder the terms: 2000 + -10000x + -1x + 5x2 = 0 Combine like terms: -10000x + -1x = -10001x 2000 + -10001x + 5x2 = 0 Solving 2000 + -10001x + 5x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -5x)(2000 + -1x) = 0Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Subproblem 2
Set the factor '(2000 + -1x)' equal to zero and attempt to solve: Simplifying 2000 + -1x = 0 Solving 2000 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2000' to each side of the equation. 2000 + -2000 + -1x = 0 + -2000 Combine like terms: 2000 + -2000 = 0 0 + -1x = 0 + -2000 -1x = 0 + -2000 Combine like terms: 0 + -2000 = -2000 -1x = -2000 Divide each side by '-1'. x = 2000 Simplifying x = 2000Solution
x = {0.2, 2000}
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