## icalibear one year ago sqrt 3a+ 1 = a-3 Solve for a

1. icalibear

$\sqrt{3a+1}= a - 3$

2. egbeach

how do you get rid of a square root?

3. icalibear

square root both sides?

4. icalibear

i mean square both sides

5. egbeach

correct. what do you get when you do that?

6. icalibear

$3a + 1 = a^2 + 9$

7. egbeach

you should actually get $3a+1=\left( a-3 \right)^{2}$ you want to square it all together

8. icalibear

oh okay, and then FOIL that?

9. egbeach

yep what do you get after you FOIL?

10. icalibear

$(a - 3)(a-3)$ $a^2 - 3a - 3a + 9$ $a^2 - 6 + 9$

11. icalibear

6a not 6

12. egbeach

okay good. so now the whole equation is $3a+1= a ^{2}-6a+9$ Now set the eqation to 0

13. icalibear

$a^2 - 6a + 9 - 3a - 1 = 0$

14. egbeach

simplfy

15. icalibear

$a^2 - 9a + 10 = 0$

16. egbeach

9-1+8 not 10

17. icalibear

oh i thought it wa 9 - (-1)

18. egbeach

= 8*

19. icalibear

$a^2 - 9a + 8 = 0$

20. egbeach

yep. can you factor it out by yourself or do you need help?

21. icalibear

do i use an 8 and a 1

22. egbeach

yep!

23. icalibear

$(a-8)(a+1)$ $(a - 8) = 0$ $a = 8$ $(a+1) = 0$ $a =-1$

24. egbeach

it should be (a-1)=0 so both answers will be positive

25. icalibear

oh okay. thanks

26. egbeach

welcome