## boomerang285 3 years ago sqrt x+10 = x-2

1. boomerang285

$\sqrt{x+10}=x-2$

2. Nameless

you first need to get rid of the radical.

3. Nameless

so square both sides.

4. boomerang285

ok

5. Nameless

so you should have x+10 = x^2-4x-4 ?

6. Nameless

now move your terms all to one side and set it equal to 0 and factor or use the quadratic to solve for x

7. boomerang285

ok

8. Nameless

actualy... i typoed.. it should be $x+10=x^{2}-4x+4$

9. boomerang285

ok i was confused trying to work that out

10. Nameless

and the only reason i move to the right is cause I dont want to multiply by a negative 1.

11. Nameless

$x ^{2}-5x-6=0$

12. Nameless

you know how to factor or do the quadratic?

13. boomerang285

i have my text book here, these confuse me so much

14. Nameless

ok. i would factor this. so you set up parens.. ( )( ) right? fill them with (x )(x ). now we are looking for 2 numbers that multiply to 6 and add to -5

15. Nameless

so 2 and 3 seem to work nice.. but they are not gonna get us to where we want because of the negative 5. so we try 1 and 6. (x 1)(x 6) right?

16. boomerang285

so 2 and 3

17. boomerang285

ok

18. Nameless

now since we know we a negative 5.. we know that 6 has to be negative. so (x+1)(x-6)

19. boomerang285

so (x+1)(x-6)

20. Nameless

solve those as separate equations .. x-6=0 and x+1=0

21. boomerang285

x=6 x=-1

22. Nameless

yep. now.. the most important.. you need to plus these numbers back into the equation.. to check if both answers work.

23. boomerang285

ok

24. Nameless

$\sqrt{-1+10} =-1 - 2$

25. Nameless

$\sqrt{6+10} = 6-2$

26. boomerang285

sqrt9=-3 sqrt16 = 4

27. Nameless

so x = 6 is your only answer? does that make sense?

28. Nameless

$\sqrt{9} =3 \neq -1-2 = -3$ $\sqrt{16}=4 = 6-2=4$