Question

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

Answer 1

C) 7

Explanation:

Quadratic equation

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

`ax^2+bx+c=0`

To rewrite the equation in the form

`(x-p)^2=q`

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

`x^2+18x+74=0`

The second term can be seen as

`2(x)(9)`

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

`x^2+2(x)(9)+81-81+74=0`

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

`(x+9)^2-7=0`

Rearranging

`(x+9)^2=7`

Comparing with the general form written above, we find that

`\boxed{q=7}`