Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 0,4(x-3)-1,6=5(0,1x-0,5)
-
Equation x-243=x/2-51
-
Equation x^3-2*x^2+x+3=0
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Equation 2*sin(x)-3*cos(x)=0
- Express {x} in terms of y where:
- 5*x-15*y=13
- 18*x-15*y=-7
- 14*x-4*y=14
- 13*x+12*y=7
- Derivative of:
- a*x+b
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Identical expressions
- a*x+b=c
- a multiply by x plus b equally c
- ax+b=c
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Similar expressions
- (2x)^3+ax+bx+12=0
- a*x-b=c
a*x+b=c equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the linear equation:
Divide both parts of the equation by (b + a*x)/x
We get the answer: x = (c - b)/a
a*x+b = c
Divide both parts of the equation by (b + a*x)/x
x = c / ((b + a*x)/x)
We get the answer: x = (c - b)/a
The solution of the parametric equation
Given the equation with a parameter:
$$a x + b = c$$
Коэффициент при x равен
$$a$$
then possible cases for a :
$$a < 0$$
$$a = 0$$
Consider all cases in more detail:
With
$$a < 0$$
the equation
$$b - c - x = 0$$
its solution
$$x = b - c$$
With
$$a = 0$$
the equation
$$b - c = 0$$
its solution
$$a x + b = c$$
Коэффициент при x равен
$$a$$
then possible cases for a :
$$a < 0$$
$$a = 0$$
Consider all cases in more detail:
With
$$a < 0$$
the equation
$$b - c - x = 0$$
its solution
$$x = b - c$$
With
$$a = 0$$
the equation
$$b - c = 0$$
its solution
The graph
Sum and product of roots
[src]
sum
/(-im(b) + im(c))*re(a) (-re(b) + re(c))*im(a)\ (-im(b) + im(c))*im(a) (-re(b) + re(c))*re(a) I*|---------------------- - ----------------------| + ---------------------- + ---------------------- | 2 2 2 2 | 2 2 2 2 \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$i \left(- \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
/(-im(b) + im(c))*re(a) (-re(b) + re(c))*im(a)\ (-im(b) + im(c))*im(a) (-re(b) + re(c))*re(a) I*|---------------------- - ----------------------| + ---------------------- + ---------------------- | 2 2 2 2 | 2 2 2 2 \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$i \left(- \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
product
/(-im(b) + im(c))*re(a) (-re(b) + re(c))*im(a)\ (-im(b) + im(c))*im(a) (-re(b) + re(c))*re(a) I*|---------------------- - ----------------------| + ---------------------- + ---------------------- | 2 2 2 2 | 2 2 2 2 \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$i \left(- \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
I*((-re(c) + re(b))*im(a) - (-im(c) + im(b))*re(a)) - (-im(c) + im(b))*im(a) - (-re(c) + re(b))*re(a)
-----------------------------------------------------------------------------------------------------
2 2
im (a) + re (a)
$$\frac{i \left(\left(\operatorname{re}{\left(b\right)} - \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)} - \left(\operatorname{im}{\left(b\right)} - \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}\right) - \left(\operatorname{re}{\left(b\right)} - \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(b\right)} - \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
(i*((-re(c) + re(b))*im(a) - (-im(c) + im(b))*re(a)) - (-im(c) + im(b))*im(a) - (-re(c) + re(b))*re(a))/(im(a)^2 + re(a)^2)
Rapid solution
[src]
/(-im(b) + im(c))*re(a) (-re(b) + re(c))*im(a)\ (-im(b) + im(c))*im(a) (-re(b) + re(c))*re(a)
x1 = I*|---------------------- - ----------------------| + ---------------------- + ----------------------
| 2 2 2 2 | 2 2 2 2
\ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$x_{1} = i \left(- \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
x1 = i*(-(-re(b) + re(c))*im(a)/(re(a)^2 + im(a)^2) + (-im(b) + im(c))*re(a)/(re(a)^2 + im(a)^2)) + (-re(b) + re(c))*re(a)/(re(a)^2 + im(a)^2) + (-im(b) + im(c))*im(a)/(re(a)^2 + im(a)^2)