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Simplifying 200x + -2x2 = -1x2 + 20x + 4500 Reorder the terms: 200x + -2x2 = 4500 + 20x + -1x2 Solving 200x + -2x2 = 4500 + 20x + -1x2 Solving for variable 'x'. Reorder the terms: -4500 + 200x + -20x + -2x2 + x2 = 4500 + 20x + -1x2 + -4500 + -20x + x2 Combine like terms: 200x + -20x = 180x -4500 + 180x + -2x2 + x2 = 4500 + 20x + -1x2 + -4500 + -20x + x2 Combine like terms: -2x2 + x2 = -1x2 -4500 + 180x + -1x2 = 4500 + 20x + -1x2 + -4500 + -20x + x2 Reorder the terms: -4500 + 180x + -1x2 = 4500 + -4500 + 20x + -20x + -1x2 + x2 Combine like terms: 4500 + -4500 = 0 -4500 + 180x + -1x2 = 0 + 20x + -20x + -1x2 + x2 -4500 + 180x + -1x2 = 20x + -20x + -1x2 + x2 Combine like terms: 20x + -20x = 0 -4500 + 180x + -1x2 = 0 + -1x2 + x2 -4500 + 180x + -1x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -4500 + 180x + -1x2 = 0 Factor a trinomial. (-150 + x)(30 + -1x) = 0Subproblem 1
Set the factor '(-150 + x)' equal to zero and attempt to solve: Simplifying -150 + x = 0 Solving -150 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = 0 + 150 Combine like terms: -150 + 150 = 0 0 + x = 0 + 150 x = 0 + 150 Combine like terms: 0 + 150 = 150 x = 150 Simplifying x = 150Subproblem 2
Set the factor '(30 + -1x)' equal to zero and attempt to solve: Simplifying 30 + -1x = 0 Solving 30 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -1x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1x = 0 + -30 -1x = 0 + -30 Combine like terms: 0 + -30 = -30 -1x = -30 Divide each side by '-1'. x = 30 Simplifying x = 30Solution
x = {150, 30}
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