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Popular >

solvefor x,1-2xy+y^2=-x^2-1+2xy

Solution

solve for

x, 1 - 2 x y + y^{2} = - x^{2} - 1 + 2 x y

Solution

x = 2 y - 3 y^{2} - 2, x = 2 y + 3 y^{2} - 2

Solution steps

1 - 2 x y + y^{2} = - x^{2} - 1 + 2 x y

Switch sides

- x^{2} - 1 + 2 x y = 1 - 2 x y + y^{2}

Move

y^{2}

to the left side

- x^{2} - 1 + 2 x y - y^{2} = 1 - 2 x y

Move

2 x y

to the left side

- y^{2} + 4 x y - x^{2} - 1 = 1

Move

1

to the left side

- y^{2} + 4 x y - x^{2} - 2 = 0

Write in the standard form

a x^{2} + b x + c = 0

- x^{2} + 4 y x - y^{2} - 2 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 4 y \pm ( 4 y ) ^{2} - 4 ( - 1 ) ( - y ^{2} - 2 )}{2 ( - 1 )}

Simplify

(4 y)^{2} - 4 (- 1) (- y^{2} - 2) : 2 3 y^{2} - 2

x_{1, 2} = \frac{- 4 y \pm 2 3 y ^{2} - 2}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 4 y + 2 3 y ^{2} - 2}{2 ( - 1 )}, x_{2} = \frac{- 4 y - 2 3 y ^{2} - 2}{2 ( - 1 )}

x = \frac{- 4 y + 2 3 y ^{2} - 2}{2 ( - 1 )} : 2 y - 3 y^{2} - 2

x = \frac{- 4 y - 2 3 y ^{2} - 2}{2 ( - 1 )} : 2 y + 3 y^{2} - 2

The solutions to the quadratic equation are:

x = 2 y - 3 y^{2} - 2, x = 2 y + 3 y^{2} - 2

Popular Examples

3 x^{2} - 16 x + 23 = 0

3 x^{2} = 5 + 8 x

(x + 7)^{2} = 16

9 x^{2} + 25 = - 30 x

solvefor y,x^2+4y^2=4 solve for

y, x^{2} + 4 y^{2} = 4