Mathematics
         
语言：中文    Language:English
                                Equations   
Fold
                                Unary equation
                                Multivariate equation
                                Math OP  
Unfold
                                Linear algebra      
Unfold
                                Derivative function
                                Function image
                                Hot issues
On line Solution of Monovariate Equation：
    Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
    It supports equations that contain mathematical functions.
    Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer
    Overview: 1 questions will be solved this time.Among them
           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation （10-2x）（10-2x） = （20/3-4/3x）（12-4/3x） .
    Question type: Equation
    Solution:Original question:
     (10 − 2 x )(10 − 2 x ) = (20 ÷ 3 − 4 ÷ 3 × x )(12 − 4 ÷ 3 × x )
    Remove the bracket on the left of the equation:
     Left side of the equation = 10(10 − 2 x ) − 2 x (10 − 2 x )
                                             = 10 × 10 − 10 × 2 x − 2 x (10 − 2 x )
                                             = 100 − 20 x − 2 x (10 − 2 x )
                                             = 100 − 20 x − 2 x × 10 + 2 x × 2 x
                                             = 100 − 20 x − 20 x + 4 x x
                                             = 100 − 40 x + 4 x x
    The equation is transformed into :
     100 − 40 x + 4 x x = (20 ÷ 3 − 4 ÷ 3 × x )(12 − 4 ÷ 3 × x )
    Remove the bracket on the right of the equation:
     Right side of the equation = 20 ÷ 3 × (12 − 4 ÷ 3 × x ) − 4 ÷ 3 × x (12 − 4 ÷ 3 × x )
                                               =
20
3
(12 − 4 ÷ 3 × x ) −
4
3
 x (12 − 4 ÷ 3 × x )
                                               =
20
3
 × 12 −
20
3
 × 4 ÷ 3 × x −
4
3
 x (12 − 4 ÷ 3 × x )
                                               = 80 −
80
9
 x −
4
3
 x (12 − 4 ÷ 3 × x )
                                               = 80 −
80
9
 x −
4
3
 x × 12 +
4
3
 x × 4 ÷ 3 × x
                                               = 80 −
80
9
 x − 16 x +
16
9
 x x
                                               = 80 −
224
9
 x +
16
9
 x x
    The equation is transformed into :
     100 − 40 x + 4 x x = 80 −
224
9
 x +
16
9
 x x

    After the equation is converted into a general formula, it is converted into:
    ( 5x - 9 )( x - 5 )=0
    From
        5x - 9 = 0
        x - 5 = 0
    it is concluded that:：
        x1=
9
5
        x2=5
    
    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》


Your problem has not been solved here? Please go to the Hot Problems section！


Return