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

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

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

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

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solve for

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

x = - y, x = y + 1

Solution steps

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

Switch sides

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

Move

y

to the left side

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

Move

x

to the left side

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

Write in the standard form

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

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + y = 0 : x = - y

Solve

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

The solutions to the quadratic equation are:

x = - y, x = y + 1

(4 x + 7)^{2} = 44

35 - 6 x = 8 x^{2}

30 (p^{2} - 1) = 11 p

2 x^{2} = 10 x - 25

x^{2} - (k + 2) x + k + 1 = 0

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