# Homework Help: How do I slove this quadratic equation?

1. Mar 1, 2012

### kboynt1

1. The problem statement, all variables and given/known data

I'm studying for the GMAT and the study materials do not include how to solve this equation. I need to know how to solve it without a calculator.

2. Relevant equations

If 2^x - 2^x-2 = 3(2^13), what is the value of X?

3. The attempt at a solution

The answer key says the the answer is 15. How did they come to this?

2. Mar 1, 2012

### tiny-tim

welcome to pf!

hi kboynt1! welcome to pf!

(try using the X2 button just above the Reply box )

do you mean 2x - 2x-2 ?

hint: what is 2x/2x-2 ?

3. Mar 1, 2012

### kboynt1

Would it be 2x-(x-2)?

4. Mar 1, 2012

### tiny-tim

sure would!

and that equals … ?

5. Mar 1, 2012

### kboynt1

Holy Poop tim! my brain is about to explode... I don't know. :)

6. Mar 1, 2012

### tiny-tim

ok, when you're confused, do it one logical step at a time …

what is x - (x - 2) ?

7. Mar 1, 2012

### kboynt1

wait... is it 22x-2?

8. Mar 1, 2012

### kboynt1

or is it... 2x/x-2?

9. Mar 1, 2012

### kboynt1

so we have to simplify the left side of the equation first?

2x-2x-2=3(213)

Then

2x-(x-2)=3(213)

Then...?

10. Mar 1, 2012

### kboynt1

is it just 2?

so it's 22=4

so

4=3(213)? That doesn't seem right...

11. Mar 1, 2012

### tiny-tim

yes!

now stop trying to do both side of the equation at once

just do the LHS, and keep changing it until it matches the RHS

you have 2x/2x-2 = 4

so (2x - 2x-2)/2x-2 = … ?

12. Mar 1, 2012

### kboynt1

is it?

2x-(x-2)-2x-2-(x-2)

4-1=3

13. Mar 1, 2012

### tiny-tim

yup!

soooo … ?

14. Mar 1, 2012

### kboynt1

3(2x-2)=3(213)

divide by 3 on both sides

2x-2=213

add 2 to both the exponents

2x=215

x must equal 15.

Okay... so I'm still unclear of how you got to 3(2x-2) on the LHS I know how we got the 3 but what were the thoughts behind that and how did we retain the (2x-2)

THANK YOU BTW... Just a little more explanation/breakdown.

15. Mar 1, 2012

### tiny-tim

2x - 2x-2

= 222x - 2 - 2x-2

= (22 - 1)2x-2

16. Mar 1, 2012

### kboynt1

So what's the rule that governs the division that was done to obtain the 3 but retain the 2x-1

Sorry I'm a bit dense on this subject...

for example is the rule: xy-xz=((xy-xz)/xz)xz

17. Mar 1, 2012

### tiny-tim

the rule is AB - B = (A - 1)B