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Simplifying 2000 = -10x2 + 400x + -1000 Reorder the terms: 2000 = -1000 + 400x + -10x2 Solving 2000 = -1000 + 400x + -10x2 Solving for variable 'x'. Combine like terms: 2000 + 1000 = 3000 3000 + -400x + 10x2 = -1000 + 400x + -10x2 + 1000 + -400x + 10x2 Reorder the terms: 3000 + -400x + 10x2 = -1000 + 1000 + 400x + -400x + -10x2 + 10x2 Combine like terms: -1000 + 1000 = 0 3000 + -400x + 10x2 = 0 + 400x + -400x + -10x2 + 10x2 3000 + -400x + 10x2 = 400x + -400x + -10x2 + 10x2 Combine like terms: 400x + -400x = 0 3000 + -400x + 10x2 = 0 + -10x2 + 10x2 3000 + -400x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 3000 + -400x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(300 + -40x + x2) = 0 Factor a trinomial. 10((10 + -1x)(30 + -1x)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Subproblem 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 = {10, 30}
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