The solution to 10-6x (sqrt(59)-3)/5

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10-6x<5x^2

Solution

10 - 6 x < 5 x^{2}

x < \frac{- 59 - 3}{5} or x > \frac{59 - 3}{5}

Interval Notation

(- \infty, \frac{- 59 - 3}{5}) \cup (\frac{59 - 3}{5}, \infty)

Decimal Notation

x < - 2.13622 \dots or x > 0.93622 \dots

Solution steps

10 - 6 x < 5 x^{2}

Rewrite in standard form

10 - 6 x - 5 x^{2} < 0

Complete the square

10 - 6 x - 5 x^{2} : - 5 (x + \frac{3}{5})^{2} + \frac{59}{5}

- 5 (x + \frac{3}{5})^{2} + \frac{59}{5} < 0

Move

\frac{59}{5}

to the right side

- 5 (x + \frac{3}{5})^{2} < - \frac{59}{5}

Multiply both sides by

- 1

5 (x + \frac{3}{5})^{2} > \frac{59}{5}

Divide both sides by

5

(x + \frac{3}{5})^{2} > \frac{59}{25}

For

u^{n} > a

, if

n

is even then

x + \frac{3}{5} < - \frac{59}{25} or x + \frac{3}{5} > \frac{59}{25}

x + \frac{3}{5} < - \frac{59}{25} : x < \frac{- 59 - 3}{5}

x + \frac{3}{5} > \frac{59}{25} : x > \frac{59 - 3}{5}

Combine the intervals

x < \frac{- 59 - 3}{5} or x > \frac{59 - 3}{5}

∣ 3 x + 2 ∣ < - 7

\frac{4}{7} x + 3 = 5

4 x^{2} + 36 x = - 85

lo g_{2} (2^{8})

5 x^{2} + 9 x - 38 = 0

What is 10-6x<5x^2 ?
The solution to 10-6x<5x^2 is x<(-sqrt(59)-3)/5 \lor x>(sqrt(59)-3)/5