The expression 2x + (x - 7)^2 is equivalent to x^2 + bx+ 49 for all values of x. What is the value of b?
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.
To find the value of b, we can simplify the given expression and compare it with the expression x^2 + bx + 49.
We start with the given expression: 2x + (x - 7)^2.
Expanding (x - 7)^2, we get: (x - 7)(x - 7) = x^2 - 14x + 49.
Now we substitute this expression back into the original expression: 2x + (x^2 - 14x + 49).
Combining like terms, we have: x^2 - 14x + 2x + 49.
Simplifying further, we get: x^2 - 12x + 49.
Comparing this with x^2 + bx + 49, we see that b = -12.
Hence, the value of b is -12.