The quadratic $10x^2+100x+1000$ can be written in the form $a(x+b)^2+c$, where $a$, $b$, and $c$ are constants. What is $a+b+c$?
To write the quadratic in the form $a(x+b)^2+c$, I need to complete the square. To do that, I first factor out the coefficient of $x^2$, which is $10$, from the first two terms: $10x^2+100x+1000=10(x^2+10x)+1000$. Next, I add and subtract the square of half of the coefficient of $x$ inside the parentheses: $10(x^2+10x)+1000=10(x^2+10x+25-25)+1000=10((x+5)^2-25)+1000$. Then, I simplify the expression by distributing the $10$ and combining the constants: $10((x+5)^2-25)+1000=10(x+5)^2-250+1000=10(x+5)^2+750$. Now I can see that $a=10$, $b=5$, and $c=750$. Therefore, $a+b+c=10+5+750=765$.

