Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation |x|=5
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Equation x-cos(x)=0
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Equation a+970=69*32
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Equation t-4/25=8
- Express {x} in terms of y where:
- -18*x+16*y=4
- 10*x+3*y=11
- 14*x+17*y=9
- -7*x-17*y=-8
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Identical expressions
- 4x-(y- one)^ two = zero
- 4x minus (y minus 1) squared equally 0
- 4x minus (y minus one) to the power of two equally zero
- 4x-(y-1)2=0
- 4x-y-12=0
- 4x-(y-1)²=0
- 4x-(y-1) to the power of 2=0
- 4x-y-1^2=0
- 4x-(y-1)^2=O
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Similar expressions
- 4x+(y-1)^2=0
- 4x-(y+1)^2=0
4x-(y-1)^2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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:
$$4 x - \left(y - 1\right)^{2} + 1 = 1$$
Divide both parts of the equation by (1 - (-1 + y)^2 + 4*x)/x
We get the answer: x = (-1 + y)^2/4
4*x-(y-1)^2 = 0
Expand brackets in the left part
4*x-y+1^2 = 0
Looking for similar summands in the left part:
-(-1 + y)^2 + 4*x = 0
Move free summands (without x)
from left part to right part, we given:
$$4 x - \left(y - 1\right)^{2} + 1 = 1$$
Divide both parts of the equation by (1 - (-1 + y)^2 + 4*x)/x
x = 1 / ((1 - (-1 + y)^2 + 4*x)/x)
We get the answer: x = (-1 + y)^2/4
The graph
Rapid solution
[src]
2 2
im (y) (-1 + re(y)) I*(-1 + re(y))*im(y)
x1 = - ------ + ------------- + --------------------
4 4 2
$$x_{1} = \frac{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2}}{4} + \frac{i \left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{2} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{4}$$
x1 = (re(y) - 1)^2/4 + i*(re(y) - 1)*im(y)/2 - im(y)^2/4
Sum and product of roots
[src]
sum
2 2
im (y) (-1 + re(y)) I*(-1 + re(y))*im(y)
- ------ + ------------- + --------------------
4 4 2
$$\frac{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2}}{4} + \frac{i \left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{2} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{4}$$
=
2 2
im (y) (-1 + re(y)) I*(-1 + re(y))*im(y)
- ------ + ------------- + --------------------
4 4 2
$$\frac{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2}}{4} + \frac{i \left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{2} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{4}$$
product
2 2
im (y) (-1 + re(y)) I*(-1 + re(y))*im(y)
- ------ + ------------- + --------------------
4 4 2
$$\frac{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2}}{4} + \frac{i \left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{2} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{4}$$
=
2 2
im (y) (-1 + re(y)) I*(-1 + re(y))*im(y)
- ------ + ------------- + --------------------
4 4 2
$$\frac{\left(\operatorname{re}{\left(y\right)} - 1\right)^{2}}{4} + \frac{i \left(\operatorname{re}{\left(y\right)} - 1\right) \operatorname{im}{\left(y\right)}}{2} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{4}$$
-im(y)^2/4 + (-1 + re(y))^2/4 + i*(-1 + re(y))*im(y)/2