Math Is Fun Forum

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Completing the Square

Complete the square.

ax^2 + ba + c = 0, where a > 1.

Let me see.

Divide every term by a.

This leads to x^2 + b + (c/a) = 0

Divide middle term by 2 and then square.

So, b becomes (c/2)^2 = c^2/4.

Add (c^2/4) to right side.

x^2 + b + (c^2/4) = (c^2/4)

Factor left side.

(x + (c/2)) (x + (c/2)) = (c^2/4)

(x + (c/2))^2 = (c^2/4)

Take square root on both sides.

sqrt{(x + (c/2))^2} = sqrt{(c^2/4)}

x + (c/2) = c/2

x = c/2 - c/2

x = 0

Does this make sense? Did I make an error?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,190

Re: Completing the Square

ax^2 + ba + c = 0, where a > 1.

Did you mean ax^2 + bx + c = 0, where a > 1.

B

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

e_jane_aran

Member

Registered: 2023-09-15

Posts: 10

Re: Completing the Square

Complete the square.

ax^2 + ba + c = 0, where a > 1.

If the middle term is "ba", then there is no middle term, so the square-completion process is nothing more than isolating the one square:

Since anything can be viewed as having a zero added to it, then:

If the middle term is meant to be "bax", then try following the steps shown here: https://www.mathisfunforum.com/viewtopic.php?pid=435501#p435501

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"They are fast. Faster than you can believe. Don't turn your back. Don't look away. And most of all, don't blink." -the 10th Doctor

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Completing the Square

ax^2 + ba + c = 0, where a > 1.

Did you mean ax^2 + bx + c = 0, where a > 1.

B

It's not what I mean. I found the problem online. It is not my own created question.

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Completing the Square

Complete the square.

ax^2 + ba + c = 0, where a > 1.

If the middle term is "ba", then there is no middle term, so the square-completion process is nothing more than isolating the one square:

Since anything can be viewed as having a zero added to it, then:

If the middle term is meant to be "bax", then try following the steps shown here: https://www.mathisfunforum.com/viewtopic.php?pid=435501#p435501

Please, read what I said to Bob. This is not my own created problem. Understand? I found it online.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,190

Re: Completing the Square

Oh. Odd question then. Out of place in a completing the square chapter.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Completing the Square

Oh. Odd question then. Out of place in a completing the square chapter.

Bob

I find many OUT OF CHAPTER problems in math textbooks.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Completing the Square

Please, read what I said to Bob. This is not my own created problem. Understand? I found it online.

look at timestamps
she was probably writing response at same time so bobs wasn't visible to her yet
alos dont see how anyone coudl have know source of prob?
sry
where online?
url?

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Completing the Square

Please, read what I said to Bob. This is not my own created problem. Understand? I found it online.

look at timestamps
she was probably writing response at same time so bobs wasn't visible to her yet
alos dont see how anyone coudl have know source of prob?
sry
where online?
url?

I think the site is called Quora.