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 $a+b+c$?
+128475 10x^2+100x+1000 factor out 10
10 ( x ^2 +10x + 100) complete the square on x
10 (x^2 +10x + 25 + 100 - 25 ) factor the first three terms in the parenthses.....simplify the rest
10 [ (x + 5)^2 + 75 ]
10 ( x + 5)^2 + 750
a = 10 b = 5 c = 750
So
a + b + c = 10 + 5 + 750 = 765
