Here's the question you clicked on:
vivalakoda
Solve for x?
\[-4\sqrt{x+9}=20 \]
I know how to solve is, I'm just not sure how to get rid of the -4 in the front of the radical.
you need to remove the square from x+9 the way you do that is by squaring both side and you end up with x+9=-(20/4)^2. then solve from there.
x+9=-20/4)^2. -20/4^2 = -25 then take -25 subtract 9. you will get the answer of x=-34
it's easy to see that this has NO SOLUTION: (-4)*(-5) = 20 so that means: \(\large -4\sqrt{x+9}=20 \rightarrow \sqrt{x+9}=-5\) \(\large \sqrt{x+9}=-5\) which has no solution because the left side is always positive but the right side is negative
Can't you just square both sides to get rid of the square root, then solve like an equation?
yes you can try to do that... it's one technique you should try to solve it. but why continue when you know this is an impossible equation to solve?
not impossible, no solution... if you do solve it, the solution is an extraneous solution....
If according to your answer it is √x+9 = -5 then you'd square both sides to have: x+9 = -25 subtract 9 from both sides and get -16 as x?
Difficult equation in history
squaring both sides you get positive 25
Oh, that's right thanks so then x+9=25 subtract 9 then positive 16?
yes... now let's see if the solution of x=16 works....
\(\large (-4)(\sqrt{x+9})=20 \) \(\large (-4)(\sqrt{\color {red}{16}+9})=20 \) \(\large (-4)(\sqrt{\color {red}{25}})=20 \) \(\large -4 \cdot 5 = 20 \) \(\large -20=20 \) ???? not a true statement
so the solution of x=16 is extraneous and not really a solution.
solution \[\left| -4 \right|\]
@AntarAzri , what's the solution?
\[\left| -4 \right|\]
\(\large (-4)(\sqrt{x+9})=20 \) \(\large (-4)(\sqrt{|-4|+9})=20 \) \(\large (-4)(\sqrt{4+9})=20 \) \(\large (-4)(\sqrt{13})=20 \) x=|-4| doesn't seem to work. That's not a solution.
my oh my I have headaches because of this problem..
no no i dont mean the x |−4|=4
ok. whatever... my answer stands... NO SOLUTION to the equation: \(\large (-4)(\sqrt{x+9})=20 \) \)
\[(\left| -4 \right|)(\sqrt{16+9})=20\]
here's wolframs answer: http://www.wolframalpha.com/input/?i=solve+-4*sqrt%28x%2B9%29%3D20
http://www.wolframalpha.com/input/?i=solve+ |%E2%88%924|*sqrt%28x%2B9%29%3D20
if u don't understand my answer and expanation maybe someone else can give u a better answer... i will not argue my point further....
Do we agree that it can not be the root of a negative number gives a positive number ?
I'll see what my teacher says when she grades it. Thanks for your time