hello again everyone in this video
tutorial we are going to solve this
given equation that involves radical and
eventually we're gonna check our answer
for any extraneous solution as well so
let's go ahead and get started the very
first step I want you to make sure that
the radical has been isolated to do that
one I want you to move this negative
eight on the right-hand side so this way
we have isolated radical on the
left-hand side and X and when you move
this negative eight on the other side
becomes positive eight now we want to
get rid of this radical or the square
root by squaring both sides so far so
good so this square and square root that
undo each other we got seven X plus 50
equals two we'll be using this fact a
plus B square are simply I'll explain to
your liberal later so that's going to be
x squared plus 16x plus 64 so for the
right-hand side I use this fact so you
can look at it I showed you step by step
so let's go ahead and combine everything
on one side I want you to move this 7x
on the right-hand side and 50 on the
right-hand side so what we gonna get so
0 is gonna be on the left-hand side and
then I'm gonna have X square plus 16x
plus 64 is already on the right-hand
side when you move this 7x to the
right-hand side become negative 7x and
minus 50 as well so let's combine the
like terms X square and then 16x take
away 7 X a is plus
I x64 - 50 is plus 14 and I can put a
zero on this side that doesn't make any
difference so this is a quadratic
equation that can be easily factored out
the possible factors are can you tell me
so that is going to be X plus 2 and X
plus 7 so we can split them up so X plus
2 equal to 0 the other X plus 7 equal to
0 that means X equal to negative 2 is
one of our solution and X equal to
negative 7 another one now we're gonna
check our answer for any extraneous
solution so let's check out fast X equal
to negative 2 let's see we plug it in
wherever you see X I'm gonna just look
over there X wherever you see X replace
it by negative 2 so this is gonna happen
to 7 times negative 2 plus 50 and minus
8 my question is is it equal to negative
2 so negative 14 plus 50 the square root
minus 8 that's gonna give you 36 square
root minus 8 that's gonna give you 6
minus 8 and on the right hand side is 2
so 6 negative 8 is gonna give you
negative 2 and that was negative 2 as
well so my question is is negative 2 on
the left hand side is same as negative 2
on the right hand side yes that means we
have a true statement
thus x equals 2 negative 2 is our
solution finally we're gonna check our
answer x equals 2 negative 7 for any
extraneous solution once again we're
ucx you replace it by negative seven so
let's see what happens
so seven times negative seven plus 50
and then minus eight question mark is
this thing is it equal to negative seven
so seven times negative 7 is negative 49
plus 50 square root minus eight that's
gonna give you square root of one minus
eight that's one minus eight on the left
hand side and on the right hand side is
negative 7 is negative seven on the left
hand side is same as the right hand side
negative seven yes and the statement is
true thus X equal to negative seven is
our solution as well so that means we
got both X equal to negative two and X
equal to negative seven or both are our
solutions thanks for watching and please
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