Find the constant term that should be added to make the following expression a perfect-square trinomial. X^2+9x

Question

Can someone please help?  Find the constant term that should be added to make the following expression a perfect-square trinomial. X^2+9x

Answer 1

 X^2 + 9X

 

 X^2 + 2 ( 9/2) X +81/4 = ( X + 9/ 2) ^2

 

 

Answer 2

Hi Abby;

X^2+9x

This factors as...

(x+4.5)(x+4.5)

Let's FOIL...

FIRST...(x)(x)=x²

OUTER...(x)(4.5)=4.5x

INNER...(4.5)(x)=4.5x

LAST...(4.5)(4.5)=20.25

x²+4.5x+4.5x+20.25

x²+9x+20.25

 

This equation is of a parabola...

Ax²+Bx+C

The formula to establish C such that the equation is a perfect square is...

(B/2)²

(9/2)²

(4.5)²

20.25