welcome to premed in this video tutorial
we are going to solve this given radical
equation by this given isolation method
and eventually we're gonna check our
answer as well so let's go ahead and get
started the very first step is we want
to make sure that wherever you see this
radical part this one over here this one
I'm gonna isolate and I'm gonna put it
on the other side so once you move that
one on the other side we are left with X
plus 15 on the left-hand side equals to
eight times square root of x so finally
we got the radical part on the right
hand side now we want to remove this
radical by just simply taking the square
of this one if you take square on this
side you're gonna take the square on
this side as well
and this square X plus 15 square could
be opened up we can expand it using this
well-known formula a plus B squared
equal to a squared plus 2 a B plus B
Square but if you want to do it a little
bit different way I can show you another
way as well so X plus 15 power 2 could
be written as since power 2 means I can
write it twice so I can write X plus 15
and then X plus 15 as well we can apply
the rainbow method X time X and then
this way foil method our rainbow method
so you're gonna do this thing so that's
gonna give you x squared plus 15 X plus
15 X and finally 15 times 15 is 225
let's combine these like terms we got x
squared plus 30x plus 225 so we're gonna
go ahead and put this whatever we got we
are going to put it right here on the
left hand side so I
can put x squared plus 30x plus 225 and
on the right hand side you can see 8
power - 8 squared is going to be a 64
and this Square and square root they
cancel each other out they undo each
other so we end up with X so 64 X I want
you to move the 64 X on the left hand
side so once you move that one x squared
plus 30x plus 225 and when you move this
one I guess I become negative 64 X equal
to 0 let's combine the like terms we're
gonna move combine these 1 so I'm gonna
do say x squared minus 34 X plus 225
equal to 0 so you can see this is a
quadratic equation we can easily factor
this one out I want you to put down two
parenthesis equal to zero I want you to
put down X right up here and X and right
up here and in the next step I want you
to write down this positive 225 on the
top of this X Factor and negative 34
which is in the middle should go at the
bottom let's find the possible factors
of 225 so the possible factor is going
to be a 9 times 25 I'm gonna put down 9
times 25 is gonna give you 225 9 + 25 of
course it's gonna give you 34 only thing
is we need to fix the sign so this is
gonna be a negative sign this is going
to be negative sign so we got these two
factors so let's put down these two
factors negative 9 is going to come over
here and negative 25 is going to come
over here and now since we have our two
factors equal to 0 I can say
then I can split them up x- 9 equal to 0
and X minus 25 equal to 0 so that's
gonna give you X equal to 9 and on this
side is gonna give us X equal to 25 so
that's our solutions turn out to be X
equal to 9 and X equal to 25 in the next
step we're gonna check these solutions
and in this next step we are going to
check our these to give an answer X
equal to 9 and X equal to 25 so let's go
ahead and check X equal to 9 if it is
gonna work for us so wherever you see X
you replace that one by 9 so that is
simply gonna give us 9 minus 8 times
square root of 9 plus 15 my question is
is it equal to the right hand side which
is 0 let's simplify the left hand side 9
minus this is square root of 9 is 3 so 8
times 3 plus 15 so 9 minus 24 plus 15 so
this if you add and subtract that's
gonna give you 0 and the right hand side
0 my question is is this statement true
yes of course indeed this is true so
thus that means this X equal to 9 is our
answer that has been checked it's a good
solution so next we're gonna check X
equal to 25 so wherever you see X
replace it by 25 so this becomes 25
minus 8 times square root of 25 plus 15
is it equal to the right hand side which
is 0 let's simplify we know that the
square root of 25 is
so I can write 25 minus 8 times 5 plus
15 so this is 25 minus 40 plus 15 that
is gonna give you 0 on the left hand
side and we know 0 is on the right side
as well
my question is this statement true yes
indeed this is true so that means our x
equals 25 is also a good solution thus
our solution set turns out to be a 9 and
25 and here is your assignment can you
do the very same radical equation by
using a substitution method you can take
your time you can pause the video
luckily I have already uploaded this
video as well go ahead and check it out
and see the correct answer thanks for
watching and please don't forget to
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exciting videos bye