Question

question 6 of 10, step 1 of 1 solve the following radical equation. (sqrt{247 + 38y} - y = 16) answer separate multiple answers with commas. (y =)

Explanation:

Step1: Isolate the radical term

$\sqrt{247 + 38y} = 16 + y$

Step2: Square both sides

$(\sqrt{247 + 38y})^2 = (16 + y)^2$
$247 + 38y = y^2 + 32y + 256$

Step3: Rearrange to quadratic form

$y^2 + 32y + 256 - 38y - 247 = 0$
$y^2 - 6y + 9 = 0$

Step4: Factor the quadratic

$(y - 3)^2 = 0$

Step5: Verify the solution

Substitute $y=3$ into original equation:
$\sqrt{247 + 38(3)} - 3 = \sqrt{247 + 114} - 3 = \sqrt{361} - 3 = 19 - 3 = 16$, which matches the right-hand side.

Answer:

$3$