Let's simplify the given expression step-by-step:
[tex]\[ 8 \sqrt{6} + 7 \sqrt{5} - 6 \sqrt{5} + 3 \sqrt{x} - 3049 + 215 \][/tex]
### Step 1: Combine Like Terms Involving Square Roots
First, observe the terms involving [tex]\(\sqrt{5}\)[/tex]:
[tex]\[ 7 \sqrt{5} - 6 \sqrt{5} = (7 - 6) \sqrt{5} = 1 \sqrt{5} = \sqrt{5} \][/tex]
Now, re-write the expression incorporating this simplification:
[tex]\[ 8 \sqrt{6} + \sqrt{5} + 3 \sqrt{x} - 3049 + 215 \][/tex]
### Step 2: Simplify the Constant Terms
Next, combine the constant terms:
[tex]\[ -3049 + 215 \][/tex]
Subtract 3049 from 215:
[tex]\[ 215 - 3049 = -2834 \][/tex]
Re-write the expression with this simplification:
[tex]\[ 8 \sqrt{6} + \sqrt{5} + 3 \sqrt{x} - 2834 \][/tex]
### Step 3: Combine All Terms
Now, the expression is fully simplified since there are no more like terms to combine. The final expression is:
[tex]\[ 8 \sqrt{6} + \sqrt{5} + 3 \sqrt{x} - 2834 \][/tex]
### Final Answer
The simplified expression is:
[tex]\[ 8 \sqrt{6} + \sqrt{5} + 3 \sqrt{x} - 2834 \][/tex]
And this represents the given expression in its most simplified form.
