Question

If the quadratic equation x2+18x+74=0 is rewritten in the form (x−p)2=q, what is the value of q?

Answer 1

Answer:

C) 7

Step-by-step 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

$\boxed{q=7}$