Question

Solve x2 – 5x + 10 = 0 by completing the square.

Answer 1

x^2 – 5x + 10 = 0

Answer 2

What are your options?

Answer 3

x^2 – 5x + 10=0
If you forget the +10 bit for a bit and take a look at x^2-5x only what number you need to add to that to get a perfect square. (perfect square looks like (x+1)^2)

Answer 4

okay.

Answer 5

(x+y)^2=x^2+2xy+y^2

Answer 6

Sorry in this case more important is
(x-y)^2=x^2-2xy+y^2

Answer 7

x^2-5x This is the x bit in this case, what is should y be?

Answer 8

From these 3 parts which one is the -5x equivalent with?
x^2
-2xy
+y^2

Answer 9

x^2

Answer 10

wrong guess :)
-2xy
Think y only as a number.
-5x=-2xy
y=5/2=2.5

Answer 11

ok

Answer 12

So where are we going with this?

Answer 13

so it would be:

(x – 5/2)^2 + 15/4 = 0

Answer 14

x^2 + 10 = 5x

Answer 15

Oh yes you are right!

Answer 16

So how can you solve it now?
(x – 5/2)^2 + 15/4 = 0

Answer 17

X = 1/2 ( 5 – i sqroot 15)

Or x = 1/2 (5 + i sqroot 15)

Answer 18

thats the final answer i came up with.

Answer 19

If you allow complex numbers.
If not you can just say no real solutions

Answer 20

oh okay but is my answers correct?

Answer 21

yes

Answer 22

i just want you to check on my answers:
Solve 3x^2 – 2x – 9 = 0


3x^2 - 2x = 9

x^2 - (2/3)x = 3

(x - 1/3)^2 = 10/9


x = (1 - sqroot10)/3

x = (1 + sqroot 10)/3

Answer 23

yes