Solve the equation. $$ x-\sqrt{10-3 x}=0 $$ Select the correct choice below and, if necessary, fill in the answer box to con A. The solution set is $$ \} $$. Aimplify your answer. Use a comma to separate answers as needed.) B. There is no solution.

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To solve the equation:

$$
x - \sqrt{10 - 3x} = 0
$$

**Step 1: Isolate the Square Root**

$$
x = \sqrt{10 - 3x}
$$

**Step 2: Square Both Sides**

$$
x^2 = 10 - 3x
$$

**Step 3: Rearrange the Equation**

$$
x^2 + 3x - 10 = 0
$$

**Step 4: Solve the Quadratic Equation**

Using the quadratic formula $$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$, where $$ a = 1 $$, $$ b = 3 $$, and $$ c = -10 $$:

$$
x = \frac{-3 \pm \sqrt{9 + 40}}{2} = \frac{-3 \pm \sqrt{49}}{2} = \frac{-3 \pm 7}{2}
$$

This gives two potential solutions:

1. $$ x = \frac{4}{2} = 2 $$
2. $$ x = \frac{-10}{2} = -5 $$

**Step 5: Check for Extraneous Solutions**

- **For $$ x = 2 $$:**

$$
2 - \sqrt{10 - 3(2)} = 2 - \sqrt{4} = 2 - 2 = 0 \quad \text{✓ Valid Solution}
$$

- **For $$ x = -5 $$:**

$$
-5 - \sqrt{10 - 3(-5)} = -5 - \sqrt{25} = -5 - 5 = -10 \neq 0 \quad \text{✗ Invalid Solution}
$$

**Conclusion:**

Only $$ x = 2 $$ is a valid solution.

**Answer Choice:**

**A. The solution set is $$ \{2\} $$.**
The solution set is $$ \{2\} $$.

Solve the equation. \( x-\sqrt{10-3 x}=0 \) Select the correct choice below and, if necessary, fill in the answer box to con A. The solution set is \( \} \). Aimplify your answer. Use a comma to separate answers as needed.) B. There is no solution.

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