`[(5sqrt(7)+sqrt(7))+)4sqrt(7)+8sqrt(7))]-(19)^(2)=?`

Options

A. 143
B. `72sqrt(7)`
C. 134
D. `70sqrt(7)`

Explanation

To solve the expression \([(5\sqrt{7} + \sqrt{7}) + (4\sqrt{7} + 8\sqrt{7})] - (19)^2\), we will break it down step by step.

### Step 1: Simplify the terms inside the brackets
Combine the terms \(5\sqrt{7}\), \(\sqrt{7}\), \(4\sqrt{7}\), and \(8\sqrt{7}\).

\[ 5\sqrt{7} + \sqrt{7} = 6\sqrt{7} \]
\[ 4\sqrt{7} + 8\sqrt{7} = 12\sqrt{7} \]

Now combine these results:

\[ 6\sqrt{7} + 12\sqrt{7} = 18\sqrt{7} \]

### Step 2: Calculate \(19^2\)
Now we need to calculate \(19^2\):

\[ 19^2 = 361 \]

### Step 3: Combine the results
Now substitute back into the expression:

\[ 18\sqrt{7} - 361 \]

### Step 4: Final expression
This gives us the final expression:

\[ x = 18\sqrt{7} - 361 \]

### Step 5: Calculate \(18\sqrt{7}\)
To find a numerical value for \(18\sqrt{7}\), we can approximate \(\sqrt{7}\):

\[ \sqrt{7} \approx 2.64575 \]
\[ 18\sqrt{7} \approx 18 \times 2.64575 \approx 47.6 \]

### Step 6: Final Calculation
Now we can compute:

\[ x \approx 47.6 - 361 \approx -313.4 \]

### Final Answer
Thus, the final answer is:

\[ x = 18\sqrt{7} - 361 \]

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