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Identical expressions
- 4x+2y-4z- fifteen = zero
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Similar expressions
- 4x+2y-4z+15=0
- 4x+2y+4z-15=0
- 4x-2y-4z-15=0
4x+2y-4z-15=0 equation
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The solution
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[src]
4*x + 2*y - 4*z - 15 = 0
$$\left(- 4 z + \left(4 x + 2 y\right)\right) - 15 = 0$$
Detail solution
Given the linear equation:
Looking for similar summands in the left part:
Move free summands (without x)
from left part to right part, we given:
$$4 x + 2 y - 4 z = 15$$
Move the summands with the other variables
from left part to right part, we given:
$$4 x + 2 y = 4 z + 15$$
Divide both parts of the equation by (2*y + 4*x)/x
We get the answer: x = 15/4 + z - y/2
4*x+2*y-4*z-15 = 0
Looking for similar summands in the left part:
-15 - 4*z + 2*y + 4*x = 0
Move free summands (without x)
from left part to right part, we given:
$$4 x + 2 y - 4 z = 15$$
Move the summands with the other variables
from left part to right part, we given:
$$4 x + 2 y = 4 z + 15$$
Divide both parts of the equation by (2*y + 4*x)/x
x = 15 + 4*z / ((2*y + 4*x)/x)
We get the answer: x = 15/4 + z - y/2
The graph
Rapid solution
[src]
15 re(y) / im(y) \
x1 = -- - ----- + I*|- ----- + im(z)| + re(z)
4 2 \ 2 /
$$x_{1} = i \left(- \frac{\operatorname{im}{\left(y\right)}}{2} + \operatorname{im}{\left(z\right)}\right) - \frac{\operatorname{re}{\left(y\right)}}{2} + \operatorname{re}{\left(z\right)} + \frac{15}{4}$$
x1 = i*(-im(y)/2 + im(z)) - re(y)/2 + re(z) + 15/4
Sum and product of roots
[src]
sum
15 re(y) / im(y) \ -- - ----- + I*|- ----- + im(z)| + re(z) 4 2 \ 2 /
$$i \left(- \frac{\operatorname{im}{\left(y\right)}}{2} + \operatorname{im}{\left(z\right)}\right) - \frac{\operatorname{re}{\left(y\right)}}{2} + \operatorname{re}{\left(z\right)} + \frac{15}{4}$$
=
15 re(y) / im(y) \ -- - ----- + I*|- ----- + im(z)| + re(z) 4 2 \ 2 /
$$i \left(- \frac{\operatorname{im}{\left(y\right)}}{2} + \operatorname{im}{\left(z\right)}\right) - \frac{\operatorname{re}{\left(y\right)}}{2} + \operatorname{re}{\left(z\right)} + \frac{15}{4}$$
product
15 re(y) / im(y) \ -- - ----- + I*|- ----- + im(z)| + re(z) 4 2 \ 2 /
$$i \left(- \frac{\operatorname{im}{\left(y\right)}}{2} + \operatorname{im}{\left(z\right)}\right) - \frac{\operatorname{re}{\left(y\right)}}{2} + \operatorname{re}{\left(z\right)} + \frac{15}{4}$$
=
15 re(y) I*im(y) -- - ----- + I*im(z) - ------- + re(z) 4 2 2
$$- \frac{\operatorname{re}{\left(y\right)}}{2} + \operatorname{re}{\left(z\right)} - \frac{i \operatorname{im}{\left(y\right)}}{2} + i \operatorname{im}{\left(z\right)} + \frac{15}{4}$$
15/4 - re(y)/2 + i*im(z) - i*im(y)/2 + re(z)