What is 6<(x^2+72x+36)7 ?

The solution to 6 sqrt(8826/7)-36

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6<(x^2+72x+36)7

6 < (x^{2} + 72 x + 36) 7

x < - \frac{8826}{7} - 36 or x > \frac{8826}{7} - 36

Interval Notation

(- \infty, - \frac{8826}{7} - 36) \cup (\frac{8826}{7} - 36, \infty)

Decimal Notation

x < - 71.50855 \dots or x > - 0.49144 \dots

Solution steps

6 < (x^{2} + 72 x + 36) \cdot 7

Switch sides

(x^{2} + 72 x + 36) \cdot 7 > 6

Rewrite in standard form

7 x^{2} + 504 x + 246 > 0

Complete the square

7 x^{2} + 504 x + 246 : 7 (x + 36)^{2} - 8826

7 (x + 36)^{2} - 8826 > 0

Move

8826

to the right side

7 (x + 36)^{2} > 8826

Divide both sides by

7

(x + 36)^{2} > \frac{8826}{7}

For

u^{n} > a

, if

n

is even then

x + 36 < - \frac{8826}{7} or x + 36 > \frac{8826}{7}

x + 36 < - \frac{8826}{7} : x < - \frac{8826}{7} - 36

x + 36 > \frac{8826}{7} : x > \frac{8826}{7} - 36

Combine the intervals

x < - \frac{8826}{7} - 36 or x > \frac{8826}{7} - 36

\frac{2}{2} - \frac{1}{2}

3 a^{2} - 4 = 6 a

6 x - 47 = - 5 (x - 6)

6 x^{2} - 13 x + 5 = 0

130 + 20 x > 350

What is 6<(x^2+72x+36)7 ?
The solution to 6<(x^2+72x+36)7 is x<-sqrt(8826/7)-36\lor x>sqrt(8826/7)-36