Question

find the real solution of the following radical equation.

\\w = \sqrt{w + 18} + 2\\

\\w = ?\\

Explanation:

Isolate the radical term

$$ w - 2 = \sqrt{w + 18} $$

Square both sides and expand

$$
LATEXBLOCK0
$$

Solve the quadratic equation and check for extraneous solutions

$$
LATEXBLOCK1
$$

Checking \(w = 7\):

$$ 7 = \sqrt{7 + 18} + 2 \implies 7 = 5 + 2 \quad (\text{True}) $$

Checking \(w = -2\):

$$ -2 = \sqrt{-2 + 18} + 2 \implies -2 = 4 + 2 \quad (\text{False}) $$

Answer:

Find the real solution of the following radical equation.
\(w = \sqrt{w + 18} + 2\)
\(w =\) <blank>7</blank>