The solution to x(x+3)>5 is x (sqrt(29)-3)/2

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x(x+3)>5

Solution

x (x + 3) > 5

x < \frac{- 29 - 3}{2} or x > \frac{29 - 3}{2}

Interval Notation

(- \infty, \frac{- 29 - 3}{2}) \cup (\frac{29 - 3}{2}, \infty)

Decimal Notation

x < - 4.19258 \dots or x > 1.19258 \dots

Solution steps

x (x + 3) > 5

Rewrite in standard form

x^{2} + 3 x - 5 > 0

Complete the square

x^{2} + 3 x - 5 : (x + \frac{3}{2})^{2} - \frac{29}{4}

(x + \frac{3}{2})^{2} - \frac{29}{4} > 0

Move

\frac{29}{4}

to the right side

(x + \frac{3}{2})^{2} > \frac{29}{4}

For

u^{n} > a

, if

n

is even then

x + \frac{3}{2} < - \frac{29}{4} or x + \frac{3}{2} > \frac{29}{4}

x + \frac{3}{2} < - \frac{29}{4} : x < \frac{- 29 - 3}{2}

x + \frac{3}{2} > \frac{29}{4} : x > \frac{29 - 3}{2}

Combine the intervals

x < \frac{- 29 - 3}{2} or x > \frac{29 - 3}{2}

6 - ∣ 3 x - 2 ∣ = 5

- \frac{1}{3} + \frac{1}{3}

- 4 < x - 1 < 2

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

∣ 5 - x ∣ \geq - 6

What is x(x+3)>5 ?
The solution to x(x+3)>5 is x<(-sqrt(29)-3)/2 \lor x>(sqrt(29)-3)/2