The expression 2x + (x - 7)^2 is equivalent to x^2 + bx+ 49 for all values of x. What is the value of b?

Answer 1

Expanding (x-7)^2, we get x^2 - 14x + 49. Adding this to 2x, we get:

2x + (x-7)^2 = 2x + x^2 - 14x + 49
= x^2 - 12x + 49

We can see that this is equivalent to x^2 + bx + 49, so we must have:

b = -12

Therefore, the value of b is -12.