What is x^2-|5x+8|>0 ?

The solution to x^2-|5x+8|>0 is x (sqrt(57)+5)/2

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x^2-|5x+8|>0

x^{2} - ∣ 5 x + 8 ∣ > 0

x < \frac{- 57 + 5}{2} or x > \frac{57 + 5}{2}

Interval Notation

(- \infty, \frac{- 57 + 5}{2}) \cup (\frac{57 + 5}{2}, \infty)

Decimal Notation

x < - 1.27491 \dots or x > 6.27491 \dots

Solution steps

x^{2} - ∣ 5 x + 8 ∣ > 0

Find positive and negative intervals

x < - \frac{8}{5}, x \geq - \frac{8}{5}

Solve the inequality for each interval

x < - \frac{8}{5} or (- \frac{8}{5} \leq x < \frac{- 57 + 5}{2} or x > \frac{57 + 5}{2})

Merge Overlapping Intervals

x < \frac{- 57 + 5}{2} or x > \frac{57 + 5}{2}

\frac{- 1}{( ∣ x ∣ - 2 )} \geq 1

3 x^{2} - ∣ x - 3 ∣ > 9 x - 2

x^{2} - 2 x - 2 \geq x^{2} - 2

∣ x - 2 ∣ \leq 2 x^{2} - 9 x + 9

\frac{( x ^{2} - ∣ x ∣ - 12 )}{( x - 3 )} \geq 2 x

What is x^2-|5x+8|>0 ?
The solution to x^2-|5x+8|>0 is x<(-sqrt(57)+5)/2 \lor x>(sqrt(57)+5)/2