Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^4-8x^2+16=0
- Equation C^2x-2=21
- Equation sqrt(18-sqrt^3(x)+10)=4
- Equation |6b-9|=-20
- Express {x} in terms of y where:
- 10*x-1*y=10
- 15*x-17*y=19
- 9*x-8*y=6
- 15*x+15*y=16
- Sum of series:
-
21
- Limit of the function:
-
21
-
Identical expressions
- C^ two x-2= twenty-one
- C squared x minus 2 equally 21
- C to the power of two x minus 2 equally twenty minus one
- C2x-2=21
- C²x-2=21
- C to the power of 2x-2=21
-
Similar expressions
- C^2x+2=21
- 2*16^(x-1/-4)-6/5*12^x+9^(x+1)=0
C^2x-2=21 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the linear equation:
Move free summands (without x)
from left part to right part, we given:
$$c^{2} x = 23$$
Divide both parts of the equation by c^2
We get the answer: x = 23/c^2
c^2*x-2 = 21
Move free summands (without x)
from left part to right part, we given:
$$c^{2} x = 23$$
Divide both parts of the equation by c^2
x = 23 / (c^2)
We get the answer: x = 23/c^2
The solution of the parametric equation
Given the equation with a parameter:
$$c^{2} x - 2 = 21$$
Коэффициент при x равен
$$c^{2}$$
then possible cases for c :
$$c < 0$$
$$c = 0$$
Consider all cases in more detail:
With
$$c < 0$$
the equation
$$x - 23 = 0$$
its solution
$$x = 23$$
With
$$c = 0$$
the equation
$$-23 = 0$$
its solution
no solutions
$$c^{2} x - 2 = 21$$
Коэффициент при x равен
$$c^{2}$$
then possible cases for c :
$$c < 0$$
$$c = 0$$
Consider all cases in more detail:
With
$$c < 0$$
the equation
$$x - 23 = 0$$
its solution
$$x = 23$$
With
$$c = 0$$
the equation
$$-23 = 0$$
its solution
no solutions
The graph
Rapid solution
[src]
2 2
23*im (c) 23*re (c) 46*I*im(c)*re(c)
x1 = - ------------------ + ------------------ - ------------------
2 2 2
/ 2 2 \ / 2 2 \ / 2 2 \
\im (c) + re (c)/ \im (c) + re (c)/ \im (c) + re (c)/
$$x_{1} = \frac{23 \left(\operatorname{re}{\left(c\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}} - \frac{46 i \operatorname{re}{\left(c\right)} \operatorname{im}{\left(c\right)}}{\left(\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}} - \frac{23 \left(\operatorname{im}{\left(c\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}$$
x1 = 23*re(c)^2/(re(c)^2 + im(c)^2)^2 - 46*i*re(c)*im(c)/(re(c)^2 + im(c)^2)^2 - 23*im(c)^2/(re(c)^2 + im(c)^2)^2
Sum and product of roots
[src]
sum
2 2
23*im (c) 23*re (c) 46*I*im(c)*re(c)
- ------------------ + ------------------ - ------------------
2 2 2
/ 2 2 \ / 2 2 \ / 2 2 \
\im (c) + re (c)/ \im (c) + re (c)/ \im (c) + re (c)/
$$\frac{23 \left(\operatorname{re}{\left(c\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}} - \frac{46 i \operatorname{re}{\left(c\right)} \operatorname{im}{\left(c\right)}}{\left(\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}} - \frac{23 \left(\operatorname{im}{\left(c\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}$$
=
2 2
23*im (c) 23*re (c) 46*I*im(c)*re(c)
- ------------------ + ------------------ - ------------------
2 2 2
/ 2 2 \ / 2 2 \ / 2 2 \
\im (c) + re (c)/ \im (c) + re (c)/ \im (c) + re (c)/
$$\frac{23 \left(\operatorname{re}{\left(c\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}} - \frac{46 i \operatorname{re}{\left(c\right)} \operatorname{im}{\left(c\right)}}{\left(\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}} - \frac{23 \left(\operatorname{im}{\left(c\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}$$
product
2 2
23*im (c) 23*re (c) 46*I*im(c)*re(c)
- ------------------ + ------------------ - ------------------
2 2 2
/ 2 2 \ / 2 2 \ / 2 2 \
\im (c) + re (c)/ \im (c) + re (c)/ \im (c) + re (c)/
$$\frac{23 \left(\operatorname{re}{\left(c\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}} - \frac{46 i \operatorname{re}{\left(c\right)} \operatorname{im}{\left(c\right)}}{\left(\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}} - \frac{23 \left(\operatorname{im}{\left(c\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}$$
=
/ 2 2 \
23*\re (c) - im (c) - 2*I*im(c)*re(c)/
--------------------------------------
2
/ 2 2 \
\im (c) + re (c)/
$$\frac{23 \left(\left(\operatorname{re}{\left(c\right)}\right)^{2} - 2 i \operatorname{re}{\left(c\right)} \operatorname{im}{\left(c\right)} - \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}\right)^{2}}$$
23*(re(c)^2 - im(c)^2 - 2*i*im(c)*re(c))/(im(c)^2 + re(c)^2)^2