The solution to x^2-2x-2<0 is -sqrt(3)+1<x<sqrt(3)+1

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x^2-2x-2<0

Solution

x^{2} - 2 x - 2 < 0

- 3 + 1 < x < 3 + 1

Interval Notation

(- 3 + 1, 3 + 1)

Decimal Notation

- 0.73205 \dots < x < 2.73205 \dots

Solution steps

x^{2} - 2 x - 2 < 0

Complete the square

x^{2} - 2 x - 2 : (x - 1)^{2} - 3

(x - 1)^{2} - 3 < 0

Move

3

to the right side

(x - 1)^{2} < 3

For

u^{n} < a

, if

n

is even then

- 3 < x - 1 < 3

a < u < b

then

a < u and u < b

- 3 < x - 1 and x - 1 < 3

- 3 < x - 1 : x > - 3 + 1

x - 1 < 3 : x < 3 + 1

Combine the intervals

x > - 3 + 1 and x < 3 + 1

Merge Overlapping Intervals

- 3 + 1 < x < 3 + 1

- 6 (y + 5)^{2} = - 600

2 a^{2} + ab - 4 a - 2 b

2 x + 3 = 2

\frac{( - 8 x ^{2} y ^{2} ) ^{2}}{( 4 x ^{3} y ) ^{3}}

(- \frac{2}{5})^{3}