If the quadratic equation x2+18x+74=0 is rewritten in the form (x−p)2=q, what is the value of q?
A) −155
B) −74
C) 7
D) 9

C) 7

Step-by-step explanation:

Quadratic equation

The quadratic equation can be written in several ways, one of the most-used is

To rewrite the equation in the form

we can complete squares and rearrange the terms as follows. The provided equation is

The second term can be seen as

And the first two terms can be visualized as the square of a binomial

We have added and subtracted 81 to complete the square and not modify the equation. The new form of the equation is

Rearranging

Comparing with the general form written above, we find that