Question

Solve the radical equation.

-2 = 3Vx-4

A. X = 0
B. X = -12
C. X = -8
D. X = -4

Answer 1

To solve the radical equation \(-2 = 3\sqrt{x} - 4\), follow these steps:

1. Start by isolating the square root term:

\[
3\sqrt{x} - 4 = -2
\]

Add 4 to both sides:

\[
3\sqrt{x} = 2
\]

2. Now divide both sides by 3:

\[
\sqrt{x} = \frac{2}{3}
\]

3. Next, square both sides to eliminate the square root:

\[
x = \left(\frac{2}{3}\right)^2
\]

Calculate the square:

\[
x = \frac{4}{9}
\]

Now, let's check if there are any other values for x that could satisfy the original equation. However, since we are dealing with the case of square roots, we need to ensure \(x\) remains non-negative (and satisfies the radical). In this case, the only solution derived from the manipulation is \(x = \frac{4}{9}\).

Upon reviewing the options you've provided (A. \(X = 0\), B. \(X = -12\), C. \(X = -8\), D. \(X = -4\)), it appears none match our solution of \(x = \frac{4}{9}\).

If we need to confirm the steps or consider if there are alternative approaches that might have led to those choices, we can reconsider, but based on the current solution trail, \(x = \frac{4}{9}\) is the valid result from the equation.

None of the provided options is correct. The solution to the radical equation is \(x = \frac{4}{9}\).