What is x^2-5x+2< 1/2 ?

The solution to x^2-5x+2< 1/2 is (-sqrt(19)+5)/2 <x<(sqrt(19)+5)/2

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x^2-5x+2< 1/2

x^{2} - 5 x + 2 < \frac{1}{2}

\frac{- 19 + 5}{2} < x < \frac{19 + 5}{2}

Interval Notation

(\frac{- 19 + 5}{2}, \frac{19 + 5}{2})

Decimal Notation

0.32055 \dots < x < 4.67944 \dots

Solution steps

x^{2} - 5 x + 2 < \frac{1}{2}

Rewrite in standard form

2 x^{2} - 10 x + 3 < 0

Complete the square

2 x^{2} - 10 x + 3 : 2 (x - \frac{5}{2})^{2} - \frac{19}{2}

2 (x - \frac{5}{2})^{2} - \frac{19}{2} < 0

Move

\frac{19}{2}

to the right side

2 (x - \frac{5}{2})^{2} < \frac{19}{2}

Divide both sides by

2

(x - \frac{5}{2})^{2} < \frac{19}{4}

For

u^{n} < a

, if

n

is even then

- \frac{19}{4} < x - \frac{5}{2} < \frac{19}{4}

a < u < b

then

a < u and u < b

- \frac{19}{4} < x - \frac{5}{2} and x - \frac{5}{2} < \frac{19}{4}

- \frac{19}{4} < x - \frac{5}{2} : x > \frac{- 19 + 5}{2}

x - \frac{5}{2} < \frac{19}{4} : x < \frac{19 + 5}{2}

Combine the intervals

x > \frac{- 19 + 5}{2} and x < \frac{19 + 5}{2}

Merge Overlapping Intervals

\frac{- 19 + 5}{2} < x < \frac{19 + 5}{2}

x^{3} + 2 x^{2} - x - 2 > 0

\frac{8}{5 ( x + \frac{3}{4} )} > (\frac{4}{9} - \frac{1}{3}) \cdot (- \frac{6}{5} x)

\frac{3 x + 54}{( 2 x + 3 )} \leq 18

3 x^{2} (x - 4)^{2} < 32 - 5 (x - 2)^{2}

x^{2} - 18 > 0

What is x^2-5x+2< 1/2 ?
The solution to x^2-5x+2< 1/2 is (-sqrt(19)+5)/2 <x<(sqrt(19)+5)/2