# Thread: Need some help to prove Discriminant in a part of the quadratic equation

1. ## Need some help to prove Discriminant in a part of the quadratic equation

Hello

Im kinda stuck in a step to reshape a formula that is a part of quadratic equation:

I hope someone can give me a step by step of how its done.
Thank you very much!

hi

3. ## Re: Need some help to prove Discriminant in a part of the quadratic equation

Originally Posted by Assassinbeast

I hope someone can give me a step by step of how its done.

I do not fully understand your need,

But from what you have posted:
$\displaystyle {\left( {x + \frac{b}{{2}}} \right)^2} = \frac{{b^2}}{{4}}$

Now what?

4. ## Re: Need some help to prove Discriminant in a part of the quadratic equation

Thank you abualabed, i got it now

5. ## Re: Need some help to prove Discriminant in a part of the quadratic equation

Originally Posted by Plato
I do not fully understand your need,

But from what you have posted:
$\displaystyle {\left( {x + \frac{b}{{2}}} \right)^2} = \frac{{b^2}}{{4}}$

Now what?
It was just those two steps that i posted that i needed to know

6. ## Re: Need some help to prove Discriminant in a part of the quadratic equation

For any number, a, $\displaystyle (x+ a)^2= x^2+ 2ax+ a^2$. Comparing that to $\displaystyle x^2+ bx$ we see that we need 2a= b so that a= b/2 and then $\displaystyle a^2= \frac{b^2}{4}$. To make that a perfect square, we need to add $\displaystyle \frac{b^2}{4}$ and, of course, subtract it:
$\displaystyle x^2+ bx= x^2+ bx+ \frac{b^2}{4}- \frac{b^2}{4}= \left(x- \frac{b}{2}\right)^2- \frac{b^2}{4}$