Question

What value is added to both sides of the equation x2 - 8x = -10 in order to solve by completing the square?

Answer 1

first - do you know what "completing the square" means?

Answer 2

noo lol thats why I am so confused

Answer 3

ok, what the question is asking you to do is to write the left-hand-side of the expression in such a way that you end up with something like:\[(x-a)^2\]where 'a' is some number

Answer 4

Ok how do I get there lol like what are the steps

Answer 5

ok, so first can you please expand the expression \((x-a)^2\)

Answer 6

do you know how to do that?

Answer 7

Ok so the answers they give you
a. -8
b. 16
c. -4
d. 4
When i tried doing it out I got 16 is that correct

Answer 8

do you just want the answer or do you want to learn how to do this yourself?

Answer 9

I looked it up in a book and I understand it know more but not sure if I still did it right

Answer 10

so lets go through the steps, first can you expand \((x-a)^2\) ?

Answer 11

I don't understand what you mean

Answer 12

do you know how to expand the expression \((x-a)^2\) ?

Answer 13

What did was I remembered I had to take -8 divide it by 2 then square the answer you get and add it to both sides

Answer 14

thats a very /mechanical/ way of doing it. if you follow through the steps with me then you will end up /understanding/ how to solve problems like this.

Answer 15

okk

Answer 16

so, back to our expression, do you know how to expand \((x-a)^2\) ?. i.e. do you know how to expand this:\[(x-a)^2=(x-a)(x-a)=???\]

Answer 17

ya

Answer 18

what do you get?

Answer 19

That you have to expand it x-a^2 he (x-a)(x-a)

Answer 20

\[(x-a)^2=(x-a)(x-a)=x^2-...\]do you know what the rest of the terms on the right-hand-side should be?

Answer 21

noo

Answer 22

then you will have a lot of trouble understanding how to solve these types of problems.

Answer 23

let me show you what to do this time and hopefully you will learn for next time.

Answer 24

so, we have:\[(x-a)^2=(x-a)(x-a)=x(x-a)-a(x-a)=x^2-ax-ax+a^2\]\[\qquad=x^2-2ax+a^2\]

Answer 25

now, if we compare this to the left-hand-side of the question you were given we see you have:\[x^2-8x=...\]

Answer 26

so compare that to:\[x^2-2ax+a^2\]and you will notice that 2a must equal 8 in order to match the equation you were given.
so we can see that we must have:\[2a=8\]therefore, dividing both sides by 2 we get:\[a=4\]

Answer 27

so now we know that:\[(x-4)^2\]will give us an expression with \(x^2-8x\) in it plus some constant. if we expand this we see this comes to:\[(x-4)^2=x^2-8x+16\]

Answer 28

now since your original expression did not contain a "+16", we need to add 16 to the right hand side of your original expression to balance the equations.

Answer 29

so we end up with:\[x^2-8x=-10\]therefore:\[(x-4)^2=-10+16=6\]

Answer 30

and we end up with something on the left-hand-side which is an exact square. this is called completing the square.

Answer 31

I hope you were able to follow the steps?

Answer 32

Yes thanks so much!

Answer 33

yw