Can someone explain the technique if completing the square to transform the quadratic equation into the form (x+c)^2=a??

Question

amistre64 · Answer

a complete square is a perfect square; can you expand out the x+c part?

parthkohli · Answer

Basically, if you have something like $ax^2 + bx +  c=0$ and $ax^2 + bx + c$ is not a perfect square, you add $\left(b/2\right)^2$ to both sides to make it so.

parthkohli · Answer

If that is what you ask

anonymous · Answer

Thank you

parthkohli · Answer

Do you know WHY we do that?

anonymous · Answer

I get the ax^2+bx+c=0 but I'm not so sure about the (b/2) thing

parthkohli · Answer

It's pretty simple, in fact! Hint:$$(x + a)^2 = x^2 + (2a)x + a^2$$What do you do to get $(a)^2$ from $(2a)x$? You simply take the coefficient of $x$, divide by $2$, and square it.

parthkohli · Answer

Coefficient of $x$: ${2a}$.
Divide both sides by $2$: $a$.
Square: $a^2$.

parthkohli · Answer

That will get you the constant term.

anonymous · Answer

Okay. That part makes sense but I'm still not sure about the (b/2)^2

parthkohli · Answer

What does $b$ mean? The coefficient of $x$. What is the coefficient of $x$? $2a$...

anonymous · Answer

$$6x^2 +36x+18=0$$  So in this case, it would be 36?

parthkohli · Answer

Yes, right there!

parthkohli · Answer

Divide $36$ by $2$, square...

parthkohli · Answer

Before doing that, take $18$ to the right side of the equation to make life easier.

anonymous · Answer

So put the equation as $$6x^2+36=18$$ then do the $$(\frac{ b }{ 2 })^2$$ thing???