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Current location：Mathematical operation > History of Mathematical Computation > Answer
Overview: 1 questions will be solved this time.Among them
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation (x－50)(50＋5(100－x)) = 0 .
Question type: Equation
Solution:Original question:
| ( | x | − | 50 | ) | ( | 50 | + | 5 | ( | 100 | − | x | ) | ) | = | 0 |
| Left side of the equation = | x | ( | 50 | + | 5 | ( | 100 | − | x | ) | ) | − | 50 | ( | 50 | + | 5 | ( | 100 | − | x | ) | ) |
| = | x | × | 50 | + | x | × | 5 | ( | 100 | − | x | ) | − | 50 | ( | 50 | + | 5 | ( | 100 | − | x | ) | ) |
| = | 50 | x | + | x | × | 5 | × | 100 | − | x | × | 5 | x | − | 50 | ( | 50 | + | 5 | ( | 100 | − | x | ) | ) |
| = | 50 | x | + | x | × | 500 | − | x | × | 5 | x | − | 50 | ( | 50 | + | 5 | ( | 100 | − | x | ) | ) |
| = | 550 | x | − | x | × | 5 | x | − | 50 | ( | 50 | + | 5 | ( | 100 | − | x | ) | ) |
| = | 550 | x | − | x | × | 5 | x | − | 50 | × | 50 | − | 50 | × | 5 | ( | 100 | − | x | ) |
| = | 550 | x | − | x | × | 5 | x | − | 2500 | − | 250 | ( | 100 | − | x | ) |
| = | 550 | x | − | x | × | 5 | x | − | 2500 | − | 250 | × | 100 | + | 250 | x |
| = | 550 | x | − | x | × | 5 | x | − | 2500 | − | 25000 | + | 250 | x |
| = | 800 | x | − | x | × | 5 | x | − | 27500 |
| 800 | x | − | x | × | 5 | x | − | 27500 | = | 0 |
After the equation is converted into a general formula, it is converted into:
( x - 50 )( x - 110 )=0
From
x - 50 = 0
x - 110 = 0
it is concluded that:：
x1=50
x2=110
There are 2 solution(s).
解一元二次方程的详细方法请参阅：《一元二次方程的解法》