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Work: Find the solution of equation 6000+（80-x）*（200-10x）-10*（400-10x） = 9000 .
Question type: Equation
Solution:Original question:| | 6000 | + | ( | 80 | − | x | ) | ( | 200 | − | 10 | x | ) | − | 10 | ( | 400 | − | 10 | x | ) | = | 9000 |
Remove the bracket on the left of the equation:
| Left side of the equation = | 6000 | + | 80 | ( | 200 | − | 10 | x | ) | − | x | ( | 200 | − | 10 | x | ) | − | 10 | ( | 400 | − | 10 | x | ) |
| = | 6000 | + | 80 | × | 200 | − | 80 | × | 10 | x | − | x | ( | 200 | − | 10 | x | ) | − | 10 | ( | 400 | − | 10 | x | ) |
| = | 6000 | + | 16000 | − | 800 | x | − | x | ( | 200 | − | 10 | x | ) | − | 10 | ( | 400 | − | 10 | x | ) |
| = | 22000 | − | 800 | x | − | x | ( | 200 | − | 10 | x | ) | − | 10 | ( | 400 | − | 10 | x | ) |
| = | 22000 | − | 800 | x | − | x | × | 200 | + | x | × | 10 | x | − | 10 | ( | 400 | − | 10 | x | ) |
| = | 22000 | − | 1000 | x | + | x | × | 10 | x | − | 10 | ( | 400 | − | 10 | x | ) |
| = | 22000 | − | 1000 | x | + | x | × | 10 | x | − | 10 | × | 400 | + | 10 | × | 10 | x |
| = | 22000 | − | 1000 | x | + | x | × | 10 | x | − | 4000 | + | 100 | x |
| = | 18000 | − | 900 | x | + | x | × | 10 | x |
The equation is transformed into :
| | 18000 | − | 900 | x | + | x | × | 10 | x | = | 9000 |
The solution of the equation:
x1≈11.458980 , keep 6 decimal places
x2≈78.541020 , keep 6 decimal places
There are 2 solution(s).
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