What are the solutions to the equation solvefor y,x^2+x=y^2+y ?

The solutions to the equation solvefor y,x^2+x=y^2+y are y=x,y=-x-1

Find the zeros of solvefor y,x^2+x=y^2+y

The zeros of solvefor y,x^2+x=y^2+y are y=x,y=-x-1

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solve for

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

y = x, y = - x - 1

Solution steps

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

Switch sides

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

Move

x

to the left side

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

Move

x^{2}

to the left side

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

Factor

y^{2} + y - x - x^{2} : (y - x) (y + x + 1)

(y - x) (y + x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y - x = 0 or y + x + 1 = 0

Solve

y - x = 0 : y = x

Solve

y + x + 1 = 0 : y = - x - 1

The solutions to the quadratic equation are:

y = x, y = - x - 1

3 x^{2} + 7 x + 4 = 0

5 y^{2} + 13 y + 12 = 6

3 (x^{2} + 1) - 5 = 7

x^{2} - 2 x - 15 = - x + 5

x^{2} - 2 x - 3 = 2

What are the solutions to the equation solvefor y,x^2+x=y^2+y ?
The solutions to the equation solvefor y,x^2+x=y^2+y are y=x,y=-x-1
Find the zeros of solvefor y,x^2+x=y^2+y
The zeros of solvefor y,x^2+x=y^2+y are y=x,y=-x-1