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Simplifying 200x + -2x2 = -1x2 + 20x + 3200 Reorder the terms: 200x + -2x2 = 3200 + 20x + -1x2 Solving 200x + -2x2 = 3200 + 20x + -1x2 Solving for variable 'x'. Reorder the terms: -3200 + 200x + -20x + -2x2 + x2 = 3200 + 20x + -1x2 + -3200 + -20x + x2 Combine like terms: 200x + -20x = 180x -3200 + 180x + -2x2 + x2 = 3200 + 20x + -1x2 + -3200 + -20x + x2 Combine like terms: -2x2 + x2 = -1x2 -3200 + 180x + -1x2 = 3200 + 20x + -1x2 + -3200 + -20x + x2 Reorder the terms: -3200 + 180x + -1x2 = 3200 + -3200 + 20x + -20x + -1x2 + x2 Combine like terms: 3200 + -3200 = 0 -3200 + 180x + -1x2 = 0 + 20x + -20x + -1x2 + x2 -3200 + 180x + -1x2 = 20x + -20x + -1x2 + x2 Combine like terms: 20x + -20x = 0 -3200 + 180x + -1x2 = 0 + -1x2 + x2 -3200 + 180x + -1x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -3200 + 180x + -1x2 = 0 Factor a trinomial. (-160 + x)(20 + -1x) = 0Subproblem 1
Set the factor '(-160 + x)' equal to zero and attempt to solve: Simplifying -160 + x = 0 Solving -160 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '160' to each side of the equation. -160 + 160 + x = 0 + 160 Combine like terms: -160 + 160 = 0 0 + x = 0 + 160 x = 0 + 160 Combine like terms: 0 + 160 = 160 x = 160 Simplifying x = 160Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20Solution
x = {160, 20}
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