The solution to x^2-4x-7<0 is -sqrt(11)+2<x<sqrt(11)+2

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x^2-4x-7<0

Solution

x^{2} - 4 x - 7 < 0

- 11 + 2 < x < 11 + 2

Interval Notation

(- 11 + 2, 11 + 2)

Decimal Notation

- 1.31662 \dots < x < 5.31662 \dots

Solution steps

x^{2} - 4 x - 7 < 0

Complete the square

x^{2} - 4 x - 7 : (x - 2)^{2} - 11

(x - 2)^{2} - 11 < 0

Move

11

to the right side

(x - 2)^{2} < 11

For

u^{n} < a

, if

n

is even then

- 11 < x - 2 < 11

a < u < b

then

a < u and u < b

- 11 < x - 2 and x - 2 < 11

- 11 < x - 2 : x > - 11 + 2

x - 2 < 11 : x < 11 + 2

Combine the intervals

x > - 11 + 2 and x < 11 + 2

Merge Overlapping Intervals

- 11 + 2 < x < 11 + 2

(x^{2} - 4) (x - 1)^{6} < 0

\frac{( 6 + 3 j ) ^{2}}{( 2 - 4 j ) + 8} < 30

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

(x^{2} + 8) (x - 4) (x + 2) < 0

\frac{3}{( 1 - x )} \leq 2