Okay, let me try to figure out how to solve this equation: 441 + 2(21)(19) + 361 = x. Hmm, first, I need to remember the order of operations here. The equation has three terms: 441, 2 multiplied by 21 and 19, and then 361. So, I should calculate each part step by step.

Starting with the first term, 441. That's straightforward. Then the second term is 2 times 21 times 19. Let me compute that. So, 2 multiplied by 21 is 42, right? Then 42 multiplied by 19. Let me do that multiplication. 42 times 10 is 420, and 42 times 9 is 378. Adding those together: 420 + 378 equals 798. So, the second term is 798.

Now, the third term is 361. That's another straightforward number. So, putting it all together, the equation becomes 441 + 798 + 361. Let me add those up. First, 441 plus 798. Let's see, 441 + 700 is 1141, and then adding 98 gives me 1239. Then, adding 361 to 1239. 1239 + 300 is 1539, and then adding 61 gives me 1600. So, x should be 1600.

Wait a second, let me check if there's another way to approach this. Maybe there's a formula or identity that can simplify this calculation. The original equation is 441 + 2(21)(19) + 361. Hmm, 441 is 21 squared, right? Because 21 times 21 is 441. And 361 is 19 squared. So, the equation looks like a² + 2ab + b², which is the expansion of (a + b)². Let me confirm that.

If a is 21 and b is 19, then (21 + 19)² would be (40)², which is 1600. That matches the result I got earlier. So, that's a quicker way. Instead of calculating each term separately, I can recognize the structure of the equation as a perfect square. That would save time and reduce the chance of arithmetic errors. So, instead of 21 squared plus 2 times 21 times 19 plus 19 squared, which is (21 + 19) squared, which is 40 squared, which is 1600. That's a much more efficient method.

I think that's correct. Let me verify once more. 21 squared is 441, 19 squared is 361, and 2 times 21 times 19 is 798. Adding them all up: 441 + 798 is 1239, plus 361 is 1600. Yep, same result. So, using the algebraic identity here is the key. That's a good problem-solving strategy—look for patterns or known formulas that can simplify the calculation.

Therefore, the value of x is 1600. I think that's the answer. There's no need to check further since both methods lead to the same result. It's always good to verify using different approaches to ensure accuracy, especially when dealing with arithmetic operations that can be error-prone. But in this case, both methods confirm that x equals 1600.
Therefore, the value of $x$ is $\boxed{1600}$.
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