Solve the radical equation 400−6x3−−−−−−−−√5=4.(1 point)

Question

Responses

x=4
x equals 4

x=−213−−√3
x equals negative 2 root index 3 Start Root 13 End Root

x=−13−−√3
x equals negative root index 3 Start Root 13 End Root

x=56−−√3

Answer 1

To solve the radical equation \( \sqrt[3]{400 - 6x} = 4 \), we'll first isolate the radical expression and then eliminate the cube root by cubing both sides.

1. Start with the original equation:

   \[ \sqrt[3]{400 - 6x} = 4 \]

2. Cubing both sides yields:

   \[ 400 - 6x = 4^3 \]

   \[ 400 - 6x = 64 \]

3. Now, solve for \( x \):

   \[ 400 - 64 = 6x \]

   \[ 336 = 6x \]

   \[ x = \frac{336}{6} \]

   \[ x = 56 \]

Now, we just need to match our solution with the options provided.

The given answer choices include:

• \( x = 4 \)
• \( x = -\sqrt[3]{13} \)
• \( x = -\sqrt[3]{13} \)
• \( x = 56 \)

Thus, the solution is:

\[ \boxed{56} \]