What are the solutions to the equation completesquare z^2-2z ?

The solutions to the equation completesquare z^2-2z are (z-1)^2-1

Find the zeros of completesquare z^2-2z

The zeros of completesquare z^2-2z are (z-1)^2-1

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complete the square

z^{2} - 2 z

(z - 1)^{2} - 1

Solution steps

z^{2} - 2 z

Write

z^{2} - 2 z

in the form:

x^{2} + 2 a x + a^{2}

2 a = - 2 : a = - 1

Add and subtract

(- 1)^{2}

z^{2} - 2 z + (- 1)^{2} - (- 1)^{2}

x^{2} + 2 a x + a^{2} = (x + a)^{2}

z^{2} - 2 z + (- 1)^{2} = (z - 1)^{2}

(z - 1)^{2} - (- 1)^{2}

Simplify

(z - 1)^{2} - 1

z^{2} + 3 z - 7 = z

x^{2} + 2 x - 8 = 0

3 x^{2} - 7 = 5

7 k = 78 - k^{2}

12 x^{2} - 36 x = 0

What are the solutions to the equation completesquare z^2-2z ?
The solutions to the equation completesquare z^2-2z are (z-1)^2-1
Find the zeros of completesquare z^2-2z
The zeros of completesquare z^2-2z are (z-1)^2-1