The expression

Question

2
x
+
(
x
−
7
)
2
is equivalent to
x
2
+
b
x
+
49
for all values of
x
.

What is the value of
b
?

Answer 1

To find the value of b, we need to expand the expression 2x+(x-7)^2 and compare it to x^2+bx+49.

Expanding (x-7)^2, we get (x-7)(x-7) = x^2 - 7x - 7x + 49 = x^2 - 14x + 49.

Now, substituting the expanded form back into the expression, we have 2x + (x^2 - 14x + 49).

Combining like terms, we get x^2 - 12x + 49.

Comparing this to x^2 + bx + 49, we see that b = -12.

Therefore, the value of b is -12.