Mister Exam
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How to use it?
- Equation:
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Equation x^2+2x+1=0
-
Equation x*7=56
-
Equation x^2=-5
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Equation x*x=x
- Express {x} in terms of y where:
- -4*x+18*y=-2
- -2*x+2*y=-7
- -16*x+2*y=20
- -10*x-15*y=-2
- Sum of series:
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17
- Derivative of:
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17
- Limit of the function:
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17
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Identical expressions
- 4x(x2)-(2x three)(2x-3)= seventeen
- 4x(x2) minus (2x3)(2x minus 3) equally 17
- 4x(x2) minus (2x three)(2x minus 3) equally seventeen
- 4xx2-2x32x-3=17
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Similar expressions
- 4x(x2)-(2x3)(2x+3)=17
- 4x(x2)+(2x3)(2x-3)=17
4x(x2)-(2x3)(2x-3)=17 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
4*x*x2 - 2*x3*(2*x - 3) = 17
$$4 x x_{2} - 2 x_{3} \left(2 x - 3\right) = 17$$
Detail solution
Given the equation:
Expand expressions:
Reducing, you get:
Move free summands (without x)
from left part to right part, we given:
$$4 x x_{2} - 4 x x_{3} + 6 x_{3} = 17$$
Divide both parts of the equation by (6*x3 - 4*x*x3 + 4*x*x2)/x
We get the answer: x = (17 - 6*x3)/(4*(x2 - x3))
4*x*(x2)-(2*x3)*(2*x-3) = 17
Expand expressions:
(4*x)*x2 + 6*x3 - 4*x*x3 = 17
Reducing, you get:
-17 + 6*x3 - 4*x*x3 + 4*x*x2 = 0
Move free summands (without x)
from left part to right part, we given:
$$4 x x_{2} - 4 x x_{3} + 6 x_{3} = 17$$
Divide both parts of the equation by (6*x3 - 4*x*x3 + 4*x*x2)/x
x = 17 / ((6*x3 - 4*x*x3 + 4*x*x2)/x)
We get the answer: x = (17 - 6*x3)/(4*(x2 - x3))
The graph
Rapid solution
[src]
/ 3*(-re(x3) + re(x2))*im(x3) (17 - 6*re(x3))*(-im(x2) + im(x3)) \ (17 - 6*re(x3))*(-re(x3) + re(x2)) 3*(-im(x2) + im(x3))*im(x3)
x1 = I*|- --------------------------------------------- + ---------------------------------------------| + --------------------------------------------- + ---------------------------------------------
| / 2 2\ / 2 2\| / 2 2\ / 2 2\
\ 2*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) / 4*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) // 4*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) / 2*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) /
$$x_{1} = \frac{\left(17 - 6 \operatorname{re}{\left(x_{3}\right)}\right) \left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)}{4 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)} + i \left(\frac{\left(17 - 6 \operatorname{re}{\left(x_{3}\right)}\right) \left(- \operatorname{im}{\left(x_{2}\right)} + \operatorname{im}{\left(x_{3}\right)}\right)}{4 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)} - \frac{3 \left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right) \operatorname{im}{\left(x_{3}\right)}}{2 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)}\right) + \frac{3 \left(- \operatorname{im}{\left(x_{2}\right)} + \operatorname{im}{\left(x_{3}\right)}\right) \operatorname{im}{\left(x_{3}\right)}}{2 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)}$$
x1 = (17 - 6*re(x3))*(re(x2) - re(x3))/(4*((re(x2) - re(x3))^2 + (im(x2) - im(x3))^2)) + i*((17 - 6*re(x3))*(-im(x2) + im(x3))/(4*((re(x2) - re(x3))^2 + (im(x2) - im(x3))^2)) - 3*(re(x2) - re(x3))*im(x3)/(2*((re(x2) - re(x3))^2 + (im(x2) - im(x3))^2))) + 3*(-im(x2) + im(x3))*im(x3)/(2*((re(x2) - re(x3))^2 + (im(x2) - im(x3))^2))
Sum and product of roots
[src]
sum
/ 3*(-re(x3) + re(x2))*im(x3) (17 - 6*re(x3))*(-im(x2) + im(x3)) \ (17 - 6*re(x3))*(-re(x3) + re(x2)) 3*(-im(x2) + im(x3))*im(x3) I*|- --------------------------------------------- + ---------------------------------------------| + --------------------------------------------- + --------------------------------------------- | / 2 2\ / 2 2\| / 2 2\ / 2 2\ \ 2*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) / 4*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) // 4*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) / 2*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) /
$$\frac{\left(17 - 6 \operatorname{re}{\left(x_{3}\right)}\right) \left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)}{4 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)} + i \left(\frac{\left(17 - 6 \operatorname{re}{\left(x_{3}\right)}\right) \left(- \operatorname{im}{\left(x_{2}\right)} + \operatorname{im}{\left(x_{3}\right)}\right)}{4 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)} - \frac{3 \left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right) \operatorname{im}{\left(x_{3}\right)}}{2 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)}\right) + \frac{3 \left(- \operatorname{im}{\left(x_{2}\right)} + \operatorname{im}{\left(x_{3}\right)}\right) \operatorname{im}{\left(x_{3}\right)}}{2 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)}$$
=
/ 3*(-re(x3) + re(x2))*im(x3) (17 - 6*re(x3))*(-im(x2) + im(x3)) \ (17 - 6*re(x3))*(-re(x3) + re(x2)) 3*(-im(x2) + im(x3))*im(x3) I*|- --------------------------------------------- + ---------------------------------------------| + --------------------------------------------- + --------------------------------------------- | / 2 2\ / 2 2\| / 2 2\ / 2 2\ \ 2*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) / 4*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) // 4*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) / 2*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) /
$$\frac{\left(17 - 6 \operatorname{re}{\left(x_{3}\right)}\right) \left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)}{4 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)} + i \left(\frac{\left(17 - 6 \operatorname{re}{\left(x_{3}\right)}\right) \left(- \operatorname{im}{\left(x_{2}\right)} + \operatorname{im}{\left(x_{3}\right)}\right)}{4 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)} - \frac{3 \left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right) \operatorname{im}{\left(x_{3}\right)}}{2 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)}\right) + \frac{3 \left(- \operatorname{im}{\left(x_{2}\right)} + \operatorname{im}{\left(x_{3}\right)}\right) \operatorname{im}{\left(x_{3}\right)}}{2 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)}$$
product
/ 3*(-re(x3) + re(x2))*im(x3) (17 - 6*re(x3))*(-im(x2) + im(x3)) \ (17 - 6*re(x3))*(-re(x3) + re(x2)) 3*(-im(x2) + im(x3))*im(x3) I*|- --------------------------------------------- + ---------------------------------------------| + --------------------------------------------- + --------------------------------------------- | / 2 2\ / 2 2\| / 2 2\ / 2 2\ \ 2*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) / 4*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) // 4*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) / 2*\(-im(x3) + im(x2)) + (-re(x3) + re(x2)) /
$$\frac{\left(17 - 6 \operatorname{re}{\left(x_{3}\right)}\right) \left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)}{4 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)} + i \left(\frac{\left(17 - 6 \operatorname{re}{\left(x_{3}\right)}\right) \left(- \operatorname{im}{\left(x_{2}\right)} + \operatorname{im}{\left(x_{3}\right)}\right)}{4 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)} - \frac{3 \left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right) \operatorname{im}{\left(x_{3}\right)}}{2 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)}\right) + \frac{3 \left(- \operatorname{im}{\left(x_{2}\right)} + \operatorname{im}{\left(x_{3}\right)}\right) \operatorname{im}{\left(x_{3}\right)}}{2 \left(\left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}\right)}$$
=
-(I*(-(-17 + 6*re(x3))*(-im(x3) + im(x2)) + 6*(-re(x3) + re(x2))*im(x3)) + (-17 + 6*re(x3))*(-re(x3) + re(x2)) + 6*(-im(x3) + im(x2))*im(x3))
----------------------------------------------------------------------------------------------------------------------------------------------
2 2
4*(-im(x3) + im(x2)) + 4*(-re(x3) + re(x2))
$$- \frac{i \left(6 \left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right) \operatorname{im}{\left(x_{3}\right)} - \left(6 \operatorname{re}{\left(x_{3}\right)} - 17\right) \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)\right) + \left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right) \left(6 \operatorname{re}{\left(x_{3}\right)} - 17\right) + 6 \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right) \operatorname{im}{\left(x_{3}\right)}}{4 \left(\operatorname{re}{\left(x_{2}\right)} - \operatorname{re}{\left(x_{3}\right)}\right)^{2} + 4 \left(\operatorname{im}{\left(x_{2}\right)} - \operatorname{im}{\left(x_{3}\right)}\right)^{2}}$$
-(i*(-(-17 + 6*re(x3))*(-im(x3) + im(x2)) + 6*(-re(x3) + re(x2))*im(x3)) + (-17 + 6*re(x3))*(-re(x3) + re(x2)) + 6*(-im(x3) + im(x2))*im(x3))/(4*(-im(x3) + im(x2))^2 + 4*(-re(x3) + re(x2))^2)