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Work: Find the solution of equation 200（84-x)+5(84-x)(84-x) = 440 .
Question type: Equation
Solution:Original question:| | 200 | ( | 84 | − | x | ) | + | 5 | ( | 84 | − | x | ) | ( | 84 | − | x | ) | = | 440 |
Remove the bracket on the left of the equation:
| Left side of the equation = | 200 | × | 84 | − | 200 | x | + | 5 | ( | 84 | − | x | ) | ( | 84 | − | x | ) |
| = | 16800 | − | 200 | x | + | 5 | ( | 84 | − | x | ) | ( | 84 | − | x | ) |
| = | 16800 | − | 200 | x | + | 5 | × | 84 | ( | 84 | − | x | ) | − | 5 | x | ( | 84 | − | x | ) |
| = | 16800 | − | 200 | x | + | 420 | ( | 84 | − | x | ) | − | 5 | x | ( | 84 | − | x | ) |
| = | 16800 | − | 200 | x | + | 420 | × | 84 | − | 420 | x | − | 5 | x | ( | 84 | − | x | ) |
| = | 16800 | − | 200 | x | + | 35280 | − | 420 | x | − | 5 | x | ( | 84 | − | x | ) |
| = | 52080 | − | 620 | x | − | 5 | x | ( | 84 | − | x | ) |
| = | 52080 | − | 620 | x | − | 5 | x | × | 84 | + | 5 | x | x |
| = | 52080 | − | 620 | x | − | 420 | x | + | 5 | x | x |
The equation is transformed into :
| | 52080 | − | 1040 | x | + | 5 | x | x | = | 440 |
The solution of the equation:
x1≈81.909278 , keep 6 decimal places
x2≈126.090722 , keep 6 decimal places
There are 2 solution(s).
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