If x is a positive quantity, then what is the value of 3x, if `0.423 - 0.2 " of " 52.5 // 0.84 = x^(2) -(0.021 + 12.5)` ?

Options

A. 2
B. `1/4`
C. `1/2`
D. 1

Answer

To solve the equation given in the problem, we will follow these steps:

### Step 1: Understand the Equation
We start with the equation:
\[ 0.423 - 0.2 \text{ of } 52.5 \div 0.84 = x^2 - (0.021 + 12.5) \]

### Step 2: Calculate the Right Side
First, simplify the right side of the equation:
\[ 0.021 + 12.5 = 12.521 \]
So, the equation becomes:
\[ 0.423 - 0.2 \text{ of } 52.5 \div 0.84 = x^2 - 12.521 \]

### Step 3: Calculate the Left Side
Now, we need to calculate \( 0.2 \text{ of } 52.5 \):
\[ 0.2 \times 52.5 = 10.5 \]
Then, divide by \( 0.84 \):
\[ \frac{10.5}{0.84} = 12.5 \]
Now, substitute this value back into the equation:
\[ 0.423 - 12.5 = x^2 - 12.521 \]

### Step 4: Simplify the Left Side
Now, calculate the left side:
\[ 0.423 - 12.5 = -12.077 \]
So, we have:
\[ -12.077 = x^2 - 12.521 \]

### Step 5: Rearranging the Equation
Rearranging gives us:
\[ x^2 = -12.077 + 12.521 \]
Calculating the right side:
\[ x^2 = 0.444 \]

### Step 6: Taking the Square Root
Now, take the square root of both sides to find \( x \):
\[ x = \sqrt{0.444} \]
Calculating this gives:
\[ x \approx 0.666 \]

### Step 7: Calculate \( 3x \)
Now we need to find \( 3x \):
\[ 3x = 3 \times 0.666 \approx 1.998 \]
Rounding this gives:
\[ 3x \approx 2 \]

### Final Answer
Thus, the value of \( 3x \) is approximately:
\[ \boxed{2} \]

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