x^2+3<= 84 — step-by-step solution

Let's solve in

ℝ

x^{2} + 3 \leq 84

ⓘ We subtract

3

from both sides

x^{2} \leq 84 - 3

ⓘ Start from

84

and move back

3

on the number line:

84 - 3

81

x^{2} \leq 81

An even power only depends on the absolute value:

x^{2} \leq 81

is equivalent to

| x | \leq 9

| A | \leq B

is equivalent to

- B \leq A \leq B

-9 \leq x \leq 9

▶Solution obtained:

x \in [-9, 9]