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- Equation:
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- Equation x+538=1284
- Express {x} in terms of y where:
- (x-17)^2+(y+26)^2=16(x−17)2+(y+26)2=16.
- 5*x-5*y=20
- 8*x-7*y=-13
- 9*x+18*y=6
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Identical expressions
- (x- seventeen)^ two +(y+ twenty-six)^ two = sixteen (x− seventeen) two +(y+ twenty-six) two = sixteen .
- (x minus 17) squared plus (y plus 26) squared equally 16(x−17)2 plus (y plus 26)2 equally 16.
- (x minus seventeen) to the power of two plus (y plus twenty minus six) to the power of two equally sixteen (x− seventeen) two plus (y plus twenty minus six) two equally sixteen .
- (x-17)2+(y+26)2=16(x−17)2+(y+26)2=16.
- x-172+y+262=16x−172+y+262=16.
- (x-17)²+(y+26)²=16(x−17)2+(y+26)2=16.
- (x-17) to the power of 2+(y+26) to the power of 2=16(x−17)2+(y+26)2=16.
- x-17^2+y+26^2=16x−172+y+262=16.
-
Similar expressions
- (x-17)^2+(y-26)^2=16(x−17)2+(y+26)2=16.
- (x-17)^2+(y+26)^2=16(x−17)2-(y+26)2=16.
- (x-17)^2-(y+26)^2=16(x−17)2+(y+26)2=16.
- (x+17)^2+(y+26)^2=16(x−17)2+(y+26)2=16.
- (x-17)^2+(y+26)^2=16(x−17)2+(y-26)2=16.
Solving equations/
Express x in terms of y where you have the equation/
(x-17)^2+(y+26)^2=16(x−17)2+(y+26)2=16.
Express x in terms of y where (x-17)^2+(y+26)^2=16(x−17)2+(y+26)2=16.
The solution
You have entered
[src]
2 2 (x - 17) + (y + 26) = 16*(x - 17)*2 + (y + 26)*2
$$\left(x - 17\right)^{2} + \left(y + 26\right)^{2} = 2 \cdot 16 \left(x - 17\right) + 2 \left(y + 26\right)$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\left(x - 17\right)^{2} + \left(y + 26\right)^{2} = 2 \cdot 16 \left(x - 17\right) + 2 \left(y + 26\right)$$
to
$$\left(- 2 \cdot 16 \left(x - 17\right) - 2 \left(y + 26\right)\right) + \left(\left(x - 17\right)^{2} + \left(y + 26\right)^{2}\right) = 0$$
Expand the expression in the equation
$$\left(- 2 \cdot 16 \left(x - 17\right) - 2 \left(y + 26\right)\right) + \left(\left(x - 17\right)^{2} + \left(y + 26\right)^{2}\right) = 0$$
We get the quadratic equation
$$x^{2} - 66 x + y^{2} + 50 y + 1457 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -66$$
$$c = y^{2} + 50 y + 1457$$
, then
The equation has two roots.
or
$$x_{1} = \frac{\sqrt{- 4 y^{2} - 200 y - 1472}}{2} + 33$$
$$x_{2} = 33 - \frac{\sqrt{- 4 y^{2} - 200 y - 1472}}{2}$$
left part with negative sign.
The equation is transformed from
$$\left(x - 17\right)^{2} + \left(y + 26\right)^{2} = 2 \cdot 16 \left(x - 17\right) + 2 \left(y + 26\right)$$
to
$$\left(- 2 \cdot 16 \left(x - 17\right) - 2 \left(y + 26\right)\right) + \left(\left(x - 17\right)^{2} + \left(y + 26\right)^{2}\right) = 0$$
Expand the expression in the equation
$$\left(- 2 \cdot 16 \left(x - 17\right) - 2 \left(y + 26\right)\right) + \left(\left(x - 17\right)^{2} + \left(y + 26\right)^{2}\right) = 0$$
We get the quadratic equation
$$x^{2} - 66 x + y^{2} + 50 y + 1457 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -66$$
$$c = y^{2} + 50 y + 1457$$
, then
D = b^2 - 4 * a * c =
(-66)^2 - 4 * (1) * (1457 + y^2 + 50*y) = -1472 - 200*y - 4*y^2
The equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{\sqrt{- 4 y^{2} - 200 y - 1472}}{2} + 33$$
$$x_{2} = 33 - \frac{\sqrt{- 4 y^{2} - 200 y - 1472}}{2}$$
Rapid solution
[src]
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\-50*im(y) - 2*im(y)*re(y), -368 + im (y) - re (y) - 50*re(y)/| 4 / 2 / 2 2 \ |atan2\-50*im(y) - 2*im(y)*re(y), -368 + im (y) - re (y) - 50*re(y)/|
x1 = 33 - \/ (-50*im(y) - 2*im(y)*re(y)) + \-368 + im (y) - re (y) - 50*re(y)/ *cos|-------------------------------------------------------------------| - I*\/ (-50*im(y) - 2*im(y)*re(y)) + \-368 + im (y) - re (y) - 50*re(y)/ *sin|-------------------------------------------------------------------|
\ 2 / \ 2 /
$$x_{1} = - i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 50 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} - 50 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 368\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 50 \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} - 50 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 368 \right)}}{2} \right)} - \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 50 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} - 50 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 368\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 50 \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} - 50 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 368 \right)}}{2} \right)} + 33$$
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\-50*im(y) - 2*im(y)*re(y), -368 + im (y) - re (y) - 50*re(y)/| 4 / 2 / 2 2 \ |atan2\-50*im(y) - 2*im(y)*re(y), -368 + im (y) - re (y) - 50*re(y)/|
x2 = 33 + \/ (-50*im(y) - 2*im(y)*re(y)) + \-368 + im (y) - re (y) - 50*re(y)/ *cos|-------------------------------------------------------------------| + I*\/ (-50*im(y) - 2*im(y)*re(y)) + \-368 + im (y) - re (y) - 50*re(y)/ *sin|-------------------------------------------------------------------|
\ 2 / \ 2 /
$$x_{2} = i \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 50 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} - 50 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 368\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 50 \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} - 50 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 368 \right)}}{2} \right)} + \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 50 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} - 50 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 368\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 50 \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} - 50 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 368 \right)}}{2} \right)} + 33$$
x2 = i*((-2*re(y)*im(y) - 50*im(y))^2 + (-re(y)^2 - 50*re(y) + im(y)^2 - 368)^2)^(1/4)*sin(atan2(-2*re(y)*im(y) - 50*im(y, -re(y)^2 - 50*re(y) + im(y)^2 - 368)/2) + ((-2*re(y)*im(y) - 50*im(y))^2 + (-re(y)^2 - 50*re(y) + im(y)^2 - 368)^2)^(1/4)*cos(atan2(-2*re(y)*im(y) - 50*im(y), -re(y)^2 - 50*re(y) + im(y)^2 - 368)/2) + 33)