Question

SHOW ALL WORK

1 what is the solution of the equation
sqrt(2x+13)-5=x

2 what is the solution of the equation
3(^5sqrt((x+2)^3))+3=27

3 what is the simplest form of the radical expression
3(^3sqrt(2a)-6(^3sqrt(2a)

Thank you :)

Answer 1

If I have the brackets correct... then the answer to 1.
is...
first add 5 to both sides to obtain...
(sqrt 2x+13) = x + 5
then square both sides to undo the square root
2x + 13 = (x + 5)^2
expand the right hand side
2x + 13 = (x + 5)(x+5)
2x + 13 = x^2 + 10x + 25
then take everything to the right hand side
0 = x^2 +10x + 25 - 2x - 13
0 = x^2 +8x +12
now factor the trinomial
0 = (x +2)(x + 6)
so x+2 = 0 and x+ 6 = 0
that is x = -2 and x = -6

Answer 2

Thank you!