Mister Exam
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How to use it?
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Equation 4*x+7=0
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Identical expressions
- zero ,3x+ zero , zero 3y=0, twelve (x+y)
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Similar expressions
- 0,3x+0,03y=0,12(x-y)
- 0,3x-0,03y=0,12(x+y)
0,3x+0,03y=0,12(x+y) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
3*x 3*y 3*(x + y) --- + --- = --------- 10 100 25
$$\frac{3 x}{10} + \frac{3 y}{100} = \frac{3 \left(x + y\right)}{25}$$
Detail solution
Given the linear equation:
Expand brackets in the left part
Expand brackets in the right part
Looking for similar summands in the left part:
Looking for similar summands in the right part:
Move the summands with the other variables
from left part to right part, we given:
$$\frac{3 x}{10} = \frac{3 x}{25} + \frac{9 y}{100}$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{9 x}{50} = \frac{9 y}{100}$$
Divide both parts of the equation by 9/50
We get the answer: x = y/2
(3/10)*x+(3/100)*y = (3/25)*(x+y)
Expand brackets in the left part
3/10x+3/100y = (3/25)*(x+y)
Expand brackets in the right part
3/10x+3/100y = 3/25x+y
Looking for similar summands in the left part:
3*x/10 + 3*y/100 = 3/25x+y
Looking for similar summands in the right part:
3*x/10 + 3*y/100 = 3*x/25 + 3*y/25
Move the summands with the other variables
from left part to right part, we given:
$$\frac{3 x}{10} = \frac{3 x}{25} + \frac{9 y}{100}$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{9 x}{50} = \frac{9 y}{100}$$
Divide both parts of the equation by 9/50
x = 9*y/100 / (9/50)
We get the answer: x = y/2
The graph
Sum and product of roots
[src]
sum
re(y) I*im(y) ----- + ------- 2 2
$$\frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2}$$
=
re(y) I*im(y) ----- + ------- 2 2
$$\frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2}$$
product
re(y) I*im(y) ----- + ------- 2 2
$$\frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2}$$
=
re(y) I*im(y) ----- + ------- 2 2
$$\frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2}$$
re(y)/2 + i*im(y)/2
Rapid solution
[src]
re(y) I*im(y)
x1 = ----- + -------
2 2
$$x_{1} = \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2}$$
x1 = re(y)/2 + i*im(y)/2