What are the solutions to the equation completesquare x^2-2x-1 ?

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

Find the zeros of completesquare x^2-2x-1

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

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complete the square

x^{2} - 2 x - 1

(x - 1)^{2} - 2

Solution steps

x^{2} - 2 x - 1

Write

x^{2} - 2 x - 1

in the form:

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

2 a = - 2 : a = - 1

Add and subtract

(- 1)^{2}

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

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

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

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

Simplify

(x - 1)^{2} - 2

- 5 x^{2} + 12 x - 8 = 0

4 x^{2} = - 3 x

2 x^{2} + 7 x - 30 = 0

2 x (3 - x) = 3

- x^{2} - 7 x = 0

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