# Thread: Make a perfect square

1. ## Make a perfect square

I need to make 8x^2+36x a perfect square, which number would i add to it to do so?(this is for parametric sequences in calc 2, but i just need to know the number i use to make that part a perfect square)

2. The idea here is that you want to write an equation such that $\displaystyle a^2x^2 + bx + c^2 = (ax + c)^2$, so you have to come up with a way to solve for c and $\displaystyle c^2$. In this case you want to know $\displaystyle c^2$.One thing we know about squaring an polynomial of the form $\displaystyle (ax + c)$ is that b from above can be given by $\displaystyle b = 2ac$. Therefore in your case you can solve for c and square it to get the value you need, i.e. solve for c in the following and then square the result
$\displaystyle 36 = 2\sqrt{8}c\Rightarrow36^2 = 4\cdot 8 \cdot c^2$

3. ## you need to add

here for the given problem if we add 41 it will make a perfect square

8x2+36x+41

4. Originally Posted by upender
here for the given problem if we add 41 it will make a perfect square

8x2+36x+41
For that equation $\displaystyle b^2-4ac=-16$ so it will be ok in $\displaystyle \mathbb{C}$ but I think the OP wants a real solution

I'd use the discriminant to find c. For it to be a perfect square we know that $\displaystyle b^2-4ac=0$

$\displaystyle 36^2 = 4 \times 8 \times c$

$\displaystyle c = \frac{36^2}{32} = 40.5$