Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 81*x^3+18*x^2+x=0
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Equation 6=8-5(7x-1)
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Equation 3x=28-x
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Equation 3x=2
- Express {x} in terms of y where:
- -13*x-7*y=16
- -16*x+10*y=-11
- -2*x-15*y=-1
- -14*x+5*y=-1
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Identical expressions
- (twenty-one / five)*(x-(six / five)*y- six)-(three / two)*(two + two *y-(seventeen / five)*x)= zero
- (21 divide by 5) multiply by (x minus (6 divide by 5) multiply by y minus 6) minus (3 divide by 2) multiply by (2 plus 2 multiply by y minus (17 divide by 5) multiply by x) equally 0
- (twenty minus one divide by five) multiply by (x minus (six divide by five) multiply by y minus six) minus (three divide by two) multiply by (two plus two multiply by y minus (seventeen divide by five) multiply by x) equally zero
- (21/5)(x-(6/5)y-6)-(3/2)(2+2y-(17/5)x)=0
- 21/5x-6/5y-6-3/22+2y-17/5x=0
- (21/5)*(x-(6/5)*y-6)-(3/2)*(2+2*y-(17/5)*x)=O
- (21 divide by 5)*(x-(6 divide by 5)*y-6)-(3 divide by 2)*(2+2*y-(17 divide by 5)*x)=0
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Similar expressions
- (21/5)*(x-(6/5)*y+6)-(3/2)*(2+2*y-(17/5)*x)=0
- (21/5)*(x+(6/5)*y-6)-(3/2)*(2+2*y-(17/5)*x)=0
- (21/5)*(x-(6/5)*y-6)-(3/2)*(2-2*y-(17/5)*x)=0
- (21/5)*(x-(6/5)*y-6)-(3/2)*(2+2*y+(17/5)*x)=0
- (21/5)*(x-(6/5)*y-6)+(3/2)*(2+2*y-(17/5)*x)=0
(21/5)*(x-(6/5)*y-6)-(3/2)*(2+2*y-(17/5)*x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ 6*y \ / 17*x\
21*|x - --- - 6| 3*|2 + 2*y - ----|
\ 5 / \ 5 /
---------------- - ------------------ = 0
5 2
$$- \frac{3 \left(- \frac{17 x}{5} + \left(2 y + 2\right)\right)}{2} + \frac{21 \left(\left(x - \frac{6 y}{5}\right) - 6\right)}{5} = 0$$
Detail solution
Given the linear equation:
Expand brackets in the left part
Looking for similar summands in the left part:
Move free summands (without x)
from left part to right part, we given:
$$\frac{93 x}{10} - \frac{201 y}{25} = \frac{141}{5}$$
Move the summands with the other variables
from left part to right part, we given:
$$\frac{93 x}{10} = \frac{201 y}{25} + \frac{141}{5}$$
Divide both parts of the equation by 93/10
We get the answer: x = 94/31 + 134*y/155
(21/5)*(x-(6/5)*y-6)-(3/2)*(2+2*y-(17/5)*x) = 0
Expand brackets in the left part
21/5x+6/5y-6)-3/22+2*y+17/5x) = 0
Looking for similar summands in the left part:
-141/5 - 201*y/25 + 93*x/10 = 0
Move free summands (without x)
from left part to right part, we given:
$$\frac{93 x}{10} - \frac{201 y}{25} = \frac{141}{5}$$
Move the summands with the other variables
from left part to right part, we given:
$$\frac{93 x}{10} = \frac{201 y}{25} + \frac{141}{5}$$
Divide both parts of the equation by 93/10
x = 141/5 + 201*y/25 / (93/10)
We get the answer: x = 94/31 + 134*y/155
The graph
Sum and product of roots
[src]
sum
94 134*re(y) 134*I*im(y) -- + --------- + ----------- 31 155 155
$$\frac{134 \operatorname{re}{\left(y\right)}}{155} + \frac{134 i \operatorname{im}{\left(y\right)}}{155} + \frac{94}{31}$$
=
94 134*re(y) 134*I*im(y) -- + --------- + ----------- 31 155 155
$$\frac{134 \operatorname{re}{\left(y\right)}}{155} + \frac{134 i \operatorname{im}{\left(y\right)}}{155} + \frac{94}{31}$$
product
94 134*re(y) 134*I*im(y) -- + --------- + ----------- 31 155 155
$$\frac{134 \operatorname{re}{\left(y\right)}}{155} + \frac{134 i \operatorname{im}{\left(y\right)}}{155} + \frac{94}{31}$$
=
94 134*re(y) 134*I*im(y) -- + --------- + ----------- 31 155 155
$$\frac{134 \operatorname{re}{\left(y\right)}}{155} + \frac{134 i \operatorname{im}{\left(y\right)}}{155} + \frac{94}{31}$$
94/31 + 134*re(y)/155 + 134*i*im(y)/155
Rapid solution
[src]
94 134*re(y) 134*I*im(y)
x1 = -- + --------- + -----------
31 155 155
$$x_{1} = \frac{134 \operatorname{re}{\left(y\right)}}{155} + \frac{134 i \operatorname{im}{\left(y\right)}}{155} + \frac{94}{31}$$
x1 = 134*re(y)/155 + 134*i*im(y)/155 + 94/31