Radical Equations Quick Check

Question

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: \[ \text{x equals } 56 \]