Question

Need help to understand how to solve equations using Complete the Square for my test tomorrow.
Ex: 4x2 – 8x – 5 = 0
**The 2 after the X is suppose to be x squared**

Answer 1

(2x+1)(2x-5)= 0
2x+1 = 0 & 2x -5 = 0. Solve for x.

Answer 2

Okay thank you. Can you help me understand how you got (2x+1)(2x-5)?

Answer 3

Okay no problem. Since the equation is 4x^2 - 8x - 5. You want to figure out what numbers multiply by each other to get four. There's 1, 2 & 4. 1 & 4 don't work because the numbers have to add up to the middle term, which is -8. & 1 & 5 are the only numbers you would multiply together to get 5. Since the last term is -5, you have to determine which number is going to have the subtraction sign.

Answer 4

I was told by my college algebra professor that "4" in 4x^2-8x-5 had to be 1 in order to solve it.

Answer 5

Oh, sorry. Then you would factor out the 4(x^2 - 2x +1) -5 - 4 = 0
4 (x^2 - 2x + 1) = 9

Answer 6

I believe that is where I am suck at. The farthest I've gone with the problem is x^2 - 2x + 1= 9

Answer 7

try my way 4x^2 = (2x)^2

Answer 8

8x = 2*2x 8*2
so, we need 4 to Complete the Square

Answer 9

(2x)^2 - 2 (2x)*2 +4 -4 -5 =0
(2x)^2-8x +4 -9 =0
(2x-2)^2 =9

Answer 10

so, there are 2 options:
2x -2 =3 ---> 2x =5 --> x = 5/2
2x-2 = -3 --> 2x = -1 --> x = -1/2

Answer 11

Wow, you lost me entirely. lol I can understand the answers to them. But how you got the answer is what I don't understand. I see the work you did, which is (2x)^2 - 2 (2x)*2 +4 -4 -5 =0 etc, but I'm not quite understanding it.

Answer 12

then, I am sorry.

Answer 13

Thank You though.

Answer 14

I think I can understand what the other person's strategy was. Where exactly are you lost?

Answer 15

I don't understand how we went from 4x^2-8x-5=0 to below::
(2x)^2 - 2 (2x)*2 +4 -4 -5 =0
(2x)^2-8x +4 -9 =0
(2x-2)^2 =9
I understand the answers Loser66 gave me and I know the answers is correct, but I want to learn how to solve this equation to get to the answer.

Answer 16

I think the way he did it was factor out 2's since 2*2 = 4 & 2*4 = 8. So (2x-2)(2x-2) = 4x^2 - 8x - 4. You can't forget the -5, so it becomes (2x)^2 - 8x + 4 - 9. If that makes sense.

Answer 17

Okay, I understand now and that does make sense, but where did the 9 come from?

Answer 18

Ok. I don't really get how completing the square helps u find the answer. But I can show u how to complete square for this problem

Answer 19

1. Add 5 to both sides
4x^2 -8x=5
2. Factor the 4
4(x^2 -2x)=5
3. Complete the square
4(x^2-2x+1)=5
4. U must balance the equation since u added 4 on the left side
4(x^2-2x+1)=5+4
So
4(x^2-2x+1)=9

Answer 20

The 9 was from adding the -5 & -4.

Answer 21

Then moving it to the other side of the equal sign.

Answer 22

Wait, u can solve by finding the square. U'll just be dealing with fractions. Check the last problem it's similar ro what u have to do for ur problem

http://www.regentsprep.org/Regents/math/algtrig/ATE3/quadcompletesquare.htm

Answer 23

Thank you so much @itsonlycdeee and @nikato for helping me. Now, I understand how you guys got that far. I need to be able to Solve a quadratic equation using complete the square.
Thank you @nikato I'll click the site.

Answer 24

No problem. I'm glad to have helped in some way

Answer 25

Ur welcome. And I'm sure that site will help u a lot