Question

Can someone please solve this equation for me by completing the square?
(2x-10)^2=25

Answer 1

solve for u? u dont want to learn on your own?

Answer 2

KC?

Answer 3

yes, i was assuming that you'd show me the steps

Answer 4

I tried it but it's not working out. I solved it using the square root property but I want to know how to do it by completing the square.

Answer 5

yes mam?

Answer 6

oops i meant lern with us help in u?

Answer 7

'learn with you helping me', yes

Answer 8

(2x-10)^2=25
2x-10=sqrt(25)
2x = 5 + 10
x=15/2
x=7.5

Answer 9

No that's the square root property, I want to solve it by completing the square.

Answer 10

umm preetha y did you call for my name?

Answer 11

o sorry please excuse me preetha ji

Answer 12

you could solve this by completing the square, although it looks like its gonna be much more work, considering you would have to multiply out the left side, bring the 25 over, and then take half the coefficient of the x term.....

Answer 13

I know.

Answer 14

you still want to do it dont you

Answer 15

Yeah, I want to see.

Answer 16

It's okay if you don't want to though.

Answer 17

let us see what dasi485 comes up with before i get started

Answer 18

go ahead Lagrange

Answer 19

i'm struck between a rock and hard place.

Answer 20

alright, lets expand that left side:(2x-10)^2=25

(2x-10)(2x-10)=25
4x^2-20x-20x+100=25
subtracting 25 from both sides we got:
4x^2-40x+75=0, now this is the quadratic which we will work with

Answer 21

Now lets go ahead and take half the coefficent of the middle term, dont forget the sign, :

-10/2=-5.
Now im gonna do a little switcharoo kangaroo, we had our quadratic as, basically what we did when i factored out a 4 was divide through by 4, so check this out, i write :

4x^2-40x+75=0 as

4x^2-40x=-75 (all i did was subtract 75 from both sides)

Now i will divide through by 4, resulting in:

x^2-10x=-75/4

Answer 22

I'm guessing we forget about the part where you factored out the 4.

Answer 23

Now we determined, that half the coeffice of the middle term was -5, but what we will do here is square it, resulting in 25, next i 25 to both sides of our quadratic, like so:
x^2-10x+25=-75/4+25

Answer 24

yeah forget about factoring out the 4, just do the step where i subtract 75 from both sides and the divid through by 4 resulting in:
x^2-10x=-75/4

Answer 25

Now getting back to the problem, we now have :
x^2-10x+25=-75/4+25

Notice something about that left side, to me it looks like something that can easily be factored as:

(x-5)^2=75/4+25

Now we add the two fraction on the right side, getting the lcd and simplifying we get:

(x-5)^2=175/4

Answer 26

Now its all cake from here, we simply take the square root of both sides, keeping in mind that on the right side were gonna have a plus or minus sign