solve sqrt(x+5)=4 — step-by-step solution

Let's solve in

ℝ

\sqrt{x + 5} = 4

We isolate the square root:

\sqrt{x + 5} = 4

. Since the right side is nonnegative, square both sides:

x + 5 = 4^{2}

ⓘ A power with a positive integer exponent is a repeated product:

4^{2}

4 \cdot 4

16

x + 5 = 16

ⓘ Subtract

5

from both sides

x = 16 - 5

ⓘ Start from

16

and move back

5

on the number line:

16 - 5

11

Candidates, pending the domain check:

x = 11

Let's evaluate the domain of

\sqrt{x + 5} = 4

For the expression

\sqrt{x + 5}

to be defined, we must have:

x + 5 \geq 0

ⓘ Subtract

5

from both sides

Domain constraints:

x \geq -5

▶Solution:

x = 11