Find the solution of 3 sqrt x+5 = -9 and determine if it is an extraneous solution

x = 4 ; not extraneous
x = 4 ; extraneous
x = 0 ; extraneous
x = 0 ; not extraneous

Question

Find the solution of 3 sqrt x+5 = -9 and determine if it is an extraneous solution

x = 4 ; not extraneous
x = 4 ; extraneous
x = 0 ; extraneous
x = 0 ; not extraneous

madmerc · Answer

$$3\sqrt{x + 5}=-9$$ is what the question looks like

madmerc · Answer

@freckles please help I don't understand what this is

baru · Answer

well we can solve this equation..take 3 to rhs, square both sides blah blah...

but look at the equation carefully, we cannot get a negative value for square root. although we can solve for x and find a number, it is 'extraneous'

madmerc · Answer

? i don't understand what that means. the solution is extraneous? but what does x equal?

baru · Answer

ok...lets first solve for x
$\\sqrt{x+5} = -3 \square~ both ~sides\ x+5=9\x=4$

baru · Answer

followed?

madmerc · Answer

yeah okay ! so it's the second one, x = 4 extraneous

baru · Answer

do you understand why its extraneous?

madmerc · Answer

something to do with the solution right like its not proven right

baru · Answer

yep,
so we have $ \sqrt{x+5}=-3$

do you know any number whose square root is negative?

madmerc · Answer

no...

baru · Answer

because there isnt...
this equation actually has no solution.
but we have somehow solved for x using correct mathematical operations.
that is why the solution is called 'extraneous'