If `3xsqrt(50)-sqrt(32x^2)=sqrt(18)`, find x

Options

A. `-8sqrt2`
B. 0
C. `3/(11)`
D. `1/3`

Answer

To solve the equation \(3x\sqrt{50} - \sqrt{32x^2} = \sqrt{18}\), we will follow these steps:

### Step 1: Simplify the square roots
First, we simplify the square roots in the equation.

- \(\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}\)
- \(\sqrt{32x^2} = \sqrt{16 \times 2 \times x^2} = \sqrt{16} \cdot \sqrt{2} \cdot \sqrt{x^2} = 4x\sqrt{2}\)
- \(\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}\)

So, we can rewrite the equation as:
\[ 3x(5\sqrt{2}) - 4x\sqrt{2} = 3\sqrt{2} \]

### Step 2: Factor out \(\sqrt{2}\)
Now, we can factor out \(\sqrt{2}\) from both sides of the equation:
\[ \sqrt{2}(15x - 4x) = 3\sqrt{2} \]

### Step 3: Simplify the equation
This simplifies to:
\[ \sqrt{2}(11x) = 3\sqrt{2} \]

### Step 4: Divide both sides by \(\sqrt{2}\)
Since \(\sqrt{2}\) is common on both sides, we can divide both sides by \(\sqrt{2}\):
\[ 11x = 3 \]

### Step 5: Solve for \(x\)
Now, we can solve for \(x\) by dividing both sides by 11:
\[ x = \frac{3}{11} \]

### Final Answer
Thus, the value of \(x\) is:
\[ \boxed{\frac{3}{11}} \]

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