The solution to x^2-2x-6<0 is -sqrt(7)+1<x<sqrt(7)+1

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x^2-2x-6<0

Solution

x^{2} - 2 x - 6 < 0

- 7 + 1 < x < 7 + 1

Interval Notation

(- 7 + 1, 7 + 1)

Decimal Notation

- 1.64575 \dots < x < 3.64575 \dots

Solution steps

x^{2} - 2 x - 6 < 0

Complete the square

x^{2} - 2 x - 6 : (x - 1)^{2} - 7

(x - 1)^{2} - 7 < 0

Move

7

to the right side

(x - 1)^{2} < 7

For

u^{n} < a

, if

n

is even then

- 7 < x - 1 < 7

a < u < b

then

a < u and u < b

- 7 < x - 1 and x - 1 < 7

- 7 < x - 1 : x > - 7 + 1

x - 1 < 7 : x < 7 + 1

Combine the intervals

x > - 7 + 1 and x < 7 + 1

Merge Overlapping Intervals

- 7 + 1 < x < 7 + 1

2 x^{2} - x - 3 \leq 0

k - 3 > 1

(r - 3) (r + 2) = 0

x^{2} - 3 x - 40 \leq 0

2 7^{\frac{- 4}{3}}