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

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

Find the zeros of solvefor x,x^2-2x=z^2-2z

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

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solve for

x, x^{2} - 2 x = z^{2} - 2 z

x = z, x = - z + 2

Solution steps

x^{2} - 2 x = z^{2} - 2 z

Move

2 z

to the left side

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

Move

z^{2}

to the left side

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

Factor

x^{2} - 2 x + 2 z - z^{2} : (x - z) (x + z - 2)

(x - z) (x + z - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - z = 0 or x + z - 2 = 0

Solve

x - z = 0 : x = z

Solve

x + z - 2 = 0 : x = - z + 2

The solutions to the quadratic equation are:

x = z, x = - z + 2

- 4 x^{2} + 6 x + 1 = 0

28 + x = 100 - x^{2}

4 x^{2} - 9 - 2 (2 x - 3) + x (2 x - 3) = 0

(x - 6) (2 - x) = (x + 3)^{2} - (x - 2)^{2}

2 x (- 3 x - 4) = - 6 x

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