Question

Radical Equations Quick Check
3 of 53 of 5 Items
Question
Solve the radical equation 400−6x3−−−−−−−−√5=4
.(1 point)
Responses

x=56−−√3
x equals root index 3 Start Root 56 End Root

x=4
x equals 4

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

x=−213−−√3

Answer 1

To solve the radical equation \( \sqrt[3]{400 - 6x} = 4 \), we can start by isolating the radical and then cubing both sides to eliminate the radical.

1. Cube both sides:
\[
400 - 6x = 4^3
\]
\[
400 - 6x = 64
\]

2. Now, isolate \( x \):
\[
-6x = 64 - 400
\]
\[
-6x = -336
\]

3. Divide both sides by \(-6\):
\[
x = \frac{-336}{-6}
\]
\[
x = 56
\]

4. Therefore, our solution is \( x = 56 \).

Now, substituting back the value into the original equation can confirm this result:
- Original equation: \(\sqrt[3]{400 - 6(56)} = 4\)
- Calculation: \(\sqrt[3]{400 - 336} = \sqrt[3]{64} = 4\), which is correct.

So the final answer is:
\[
\text{x equals } 56
\]