解方程:80 * 200 + x(1000 - 10x) + 40[800 - 200 - (1000 - 10x)] = 50 * 800 + 9000
To solve this equation, we can start by simplifying both sides:
80 * 200 + x(1000 - 10x) + 40[800 - 200 - (1000 - 10x)] = 50 * 800 + 9000
16,000 + x(1000 - 10x) + 40[600 + 10x] = 40,000 + 9,000
16,000 + x(1000 - 10x) + 24,000 + 400x = 49,000
Combine like terms:
40,000 + 400x + 1000x - 10x^2 + 16,000 + 24,000 = 49,000
Collect like terms and simplify:
-10x^2 + 1400x + 80,000 = 49,000
Rearrange the equation to set it equal to zero:
-10x^2 + 1400x + 31,000 = 0
Now we can solve this quadratic equation. We can factor out -10:
-10(x^2 - 140x - 3100) = 0
Next, we can factor the quadratic equation inside the parentheses:
(x - 170)(x + 18) = 0
Now we can set each factor equal to zero and solve for x:
x - 170 = 0 or x + 18 = 0
x = 170 or x = -18
So the solutions to the equation are x = 170 and x = -18.
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