Whats x^2-2x-2

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x = 1±sqrt (3)

Step-by-step explanation:

x^2-2x-2=0

This polynomial does not factor, so we can use completing the square to solve.

Add 2 to each side

x^2-2x-2+2 = 2

x^2 - 2x = 2

b=-2

We take b/2 and then square it

-2/2 = - 1 then square it (-1) ^2 = 1

Add 1 to each side

x^2 - 2x + 1 = 2+1

The left side is equal to (x + (b/2)) ^2

(x-1) ^2 = 3

Take the square root of each side

sqrt (x-1) ^2 = ±sqrt (3)

x-1 = ±sqrt (3)

Add 1 to each side

x-1+1 = 1±sqrt (3)

x = 1±sqrt (3)

Step-by-step explanation:

1 In general, given a{x}^{2}+bx+cax

2

+ bx+c, the factored form is:

a (x-/frac{-b+/sqrt{{b}^{2}-4ac}}{2a}) (x-/frac{-b-/sqrt{{b}^{2}-4ac}}{2a

2a



-b+√

b

2

- 4ac





) (x-

2a



-b-√

b

2

- 4ac





)

2 In this case, a=1a=1, b=-2b=-2 and c=-2c=-2.

(x-/frac{2+/sqrt{{ (-2) }^{2}-4/times - 2}}{2}) (x-/frac{2-/sqrt{{ (-2) }^{2}-4/times - 2}}{2}) (x-

2



2+√

(-2)

2

- 4*-2





) (x-

2



2-√

(-2)

2

- 4*-2





)

3 Simplify.

(x-/frac{2+2/sqrt{3}}{2}) (x-/frac{2-2/sqrt{3}}{2}) (x-

2



2+2√

3





) (x-

2



2-2√

3





)

4 Factor out the common term 22.

(x-/frac{2 (1+/sqrt{3}) }{2}) (x-/frac{2-2/sqrt{3}}{2}) (x-

2



2 (1+√

3



)

) (x-

2



2-2√

3





)

5 Cancel 22.

(x - (1+/sqrt{3})) (x-/frac{2-2/sqrt{3}}{2}) (x - (1+√

3



)) (x-

2



2-2√

3





)

6 Simplify brackets.

(x-1-/sqrt{3}) (x-/frac{2-2/sqrt{3}}{2}) (x-1-√

3



) (x-

2



2-2√

3





)

7 Factor out the common term 22.

(x-1-/sqrt{3}) (x-/frac{2 (1-/sqrt{3}) }{2}) (x-1-√

3



) (x-

2



2 (1-√

3



)

)

8 Cancel 22.

(x-1-/sqrt{3}) (x - (1-/sqrt{3})) (x-1-√

3



) (x - (1-√

3



))

9 Simplify brackets.

(x-1-/sqrt{3}) (x-1+/sqrt{3}) (x-1-√

3



) (x-1+√

3



)