Mister Exam
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Identical expressions
- 3x+2y+2z+ five = zero
- 3x plus 2y plus 2z plus 5 equally 0
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- 3x+2y+2z+5=O
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Similar expressions
- 3x+2y-2z+5=0
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- 3x-2y+2z+5=0
3x+2y+2z+5=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
3*x + 2*y + 2*z + 5 = 0
$$\left(2 z + \left(3 x + 2 y\right)\right) + 5 = 0$$
Detail solution
Given the linear equation:
Looking for similar summands in the left part:
Move free summands (without z)
from left part to right part, we given:
$$3 x + 2 y + 2 z = -5$$
Move the summands with the other variables
from left part to right part, we given:
$$3 x + 2 z = \left(-2\right) y - 5$$
Divide both parts of the equation by (2*z + 3*x)/z
We get the answer: z = -5/2 - y - 3*x/2
3*x+2*y+2*z+5 = 0
Looking for similar summands in the left part:
5 + 2*y + 2*z + 3*x = 0
Move free summands (without z)
from left part to right part, we given:
$$3 x + 2 y + 2 z = -5$$
Move the summands with the other variables
from left part to right part, we given:
$$3 x + 2 z = \left(-2\right) y - 5$$
Divide both parts of the equation by (2*z + 3*x)/z
z = -5 - 2*y / ((2*z + 3*x)/z)
We get the answer: z = -5/2 - y - 3*x/2
The graph
Rapid solution
[src]
5 3*re(x) / 3*im(x)\
z1 = - - - re(y) - ------- + I*|-im(y) - -------|
2 2 \ 2 /
$$z_{1} = i \left(- \frac{3 \operatorname{im}{\left(x\right)}}{2} - \operatorname{im}{\left(y\right)}\right) - \frac{3 \operatorname{re}{\left(x\right)}}{2} - \operatorname{re}{\left(y\right)} - \frac{5}{2}$$
z1 = i*(-3*im(x)/2 - im(y)) - 3*re(x)/2 - re(y) - 5/2
Sum and product of roots
[src]
sum
5 3*re(x) / 3*im(x)\ - - - re(y) - ------- + I*|-im(y) - -------| 2 2 \ 2 /
$$i \left(- \frac{3 \operatorname{im}{\left(x\right)}}{2} - \operatorname{im}{\left(y\right)}\right) - \frac{3 \operatorname{re}{\left(x\right)}}{2} - \operatorname{re}{\left(y\right)} - \frac{5}{2}$$
=
5 3*re(x) / 3*im(x)\ - - - re(y) - ------- + I*|-im(y) - -------| 2 2 \ 2 /
$$i \left(- \frac{3 \operatorname{im}{\left(x\right)}}{2} - \operatorname{im}{\left(y\right)}\right) - \frac{3 \operatorname{re}{\left(x\right)}}{2} - \operatorname{re}{\left(y\right)} - \frac{5}{2}$$
product
5 3*re(x) / 3*im(x)\ - - - re(y) - ------- + I*|-im(y) - -------| 2 2 \ 2 /
$$i \left(- \frac{3 \operatorname{im}{\left(x\right)}}{2} - \operatorname{im}{\left(y\right)}\right) - \frac{3 \operatorname{re}{\left(x\right)}}{2} - \operatorname{re}{\left(y\right)} - \frac{5}{2}$$
=
5 3*re(x) I*(2*im(y) + 3*im(x)) - - - re(y) - ------- - --------------------- 2 2 2
$$- \frac{i \left(3 \operatorname{im}{\left(x\right)} + 2 \operatorname{im}{\left(y\right)}\right)}{2} - \frac{3 \operatorname{re}{\left(x\right)}}{2} - \operatorname{re}{\left(y\right)} - \frac{5}{2}$$
-5/2 - re(y) - 3*re(x)/2 - i*(2*im(y) + 3*im(x))/2