Question

Use the technique of completing the square to transform the quadratic equation into the form (x+c)2 = a.

2x2 – 28x + 84 = 0

Answer 1

factor out the 2 from the first 2 terms

Answer 2

Let's first factor the 2 out of this:

\(2(x^2=14x+42)=0\)

Answer 3

@precal you stole my line lol :P

Answer 4

sorry, great minds think alike but you put an equal sign instead of a minus

Answer 5

Listen to zepp

Answer 6

How do you get rid of the two, though?

Answer 7

Then you need to take the middle term's coefficient, divide it by 2, square it and you'll get the constant that's supposed to be behind it so it becomes a perfect square.

Answer 8

You divide by 2 to both side and it would vanish! :D

because 0/2=0

Answer 9

Oh lol @precal - and = are so close from each other :P

Answer 10

yes but have 2 distinct meanings in our little world of math

Answer 11

So I'm left with (x^2=14x+42) ?

Answer 12

\(2(x^2-14x+42)=0\\\frac{2(x^2-14x+42)}{2}=\frac{0}{2}\\(x^2-14x+42)=0\)

Answer 13

Exactly, now you are able to continue.

Answer 14

Is there a 0 at the end?

Answer 15

Now take the coeffient of the middle term (with 1 power), which is 14,divide by 2, (7), and square it, 49, this would be the term you should have so you could complete the square :)

Yes, it is an equation =)

Answer 16

How did I end up with (x^2=49x+42)=0?

Answer 17

but we need 49, not 42! What are we going to do?

Add 7 to get 49, but also don't forget to substract it

\(x^2-14x+42+7-7=0\)

Answer 18

Or, \(x^2-14x+42+7=0+7\)

Answer 19

x^2=14x+49=7?

Answer 20

Very good, although it's a -, not =

Answer 21

-7 or x^2-?

Answer 22

Now you are all set, you may proceed :)

x^2-

Answer 23

How?

Answer 24

Well, you got a perfect square right the, the middle term's coefficient correspond to the half of the square root of the last term (constant)

Answer 25

Do I end up with -12x+7?

Answer 26

\(x^2-14x+49=(x-7)^2\) :D

Answer 27

\(x^2-14x+49=7\\(x-7)^2=7\\(x-7)^2-7=0\)

Answer 28

Is that clear enough? If it's not, I can re-explain :)