What is (sqrt(|x+4|^2)-25)(sqrt(x^2)-9)<= 0 ?

The solution to (sqrt(|x+4|^2)-25)(sqrt(x^2)-9)<= 0 is -29<= x<=-9\lor 9<= x<= 21

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(sqrt(|x+4|^2)-25)(sqrt(x^2)-9)<= 0

(∣ x + 4 ∣^{2} - 25) (x^{2} - 9) \leq 0

- 29 \leq x \leq - 9 or 9 \leq x \leq 21

Interval Notation

[- 29, - 9] \cup [9, 21]

Solution steps

(∣ x + 4 ∣^{2} - 25) (x^{2} - 9) \leq 0

Identify the intervals

- 29 \leq x \leq - 9 or 9 \leq x \leq 21

3 (x + 4) = 18

- 4 ∣ 1 - x ∣ < - 16

x - 4 > 3 x + 8

\frac{2}{3} x + 9 < 5

x^{2} - 8 x = 72

What is (sqrt(|x+4|^2)-25)(sqrt(x^2)-9)<= 0 ?
The solution to (sqrt(|x+4|^2)-25)(sqrt(x^2)-9)<= 0 is -29<= x<=-9\lor 9<= x<= 21