Could someone please help? I am sooo confuzzled :(
-4√(x+9)=20

Question

Could someone please help? I am sooo confuzzled :(
-4√(x+9)=20

campbell_st · Answer

start by dividing both sides of the equation by -4

what do you get..?

anonymous · Answer

sqrt(x+9)=5

anonymous · Answer

Right?

campbell_st · Answer

great now square both sides of the equation 

and you made a slight error... which won't affect the answer it should be 

$$\sqrt{x + 9} = -5$$

and remember when you square a negative you get a positive number..

anonymous · Answer

Why is the 5 negative though?

anonymous · Answer

Oh! Because the 4 is negative! I was looking at it wrong.

campbell_st · Answer

its -5 because you divided a positive number by an neative number

20/(-4) = -5

anonymous · Answer

Thanks!
I think I get it now. 
Is there more to work out next? Or am I just left with sqrt(x+9)=-5?

campbell_st · Answer

ok... what did you get when you squared both sides of the equation..?

campbell_st · Answer

this is a 3 step equation...

step 1: divide by -4

step 2: square both sides

anonymous · Answer

sqrt(x+81)=25?

campbell_st · Answer

slight error... 

$$(\sqrt{x + 9})^2 = x + 9$$

the reason is to do with the index laws

a square root is a power of 1/2

so its 

$$((x + 9)^{\frac{1}{2}})^2$$

and the power of a power rule says

$$(x^a)^b = x ^{a \times  b}$$

so you need to multiply the powers 1/2 x 2 = 1

so its 

(x + 9)^1 

which means you have

x + 9 = 25

just solve for x

mertsj · Answer

There is one slight problem here:  At the very beginning when you divided both sides by -4 you got:
$$\sqrt{x+9}=-5$$

mertsj · Answer

Now that equation says that the POSITIVE square root is equal to a NEGATIVE number.  So you know right off that there is NO SOLUTION to this problem.

mertsj · Answer

And that 16 is an extraneous root

anonymous · Answer

Yes?

mertsj · Answer

So the answer is that there is no answer.

anonymous · Answer

Oh. So do I stop after dividing or do I stop after squaring both sides?

anonymous · Answer

I would write it like this...
	-4√(x+9)=20
-4√((x)+9)/4=20/4
√(x+9)2=52
√(x+81)=25
No solution

mertsj · Answer

You could stop after dividing is you noticed the problem or you could proceed to the end and find that you get an answer of 16.  Then check it and when you find it won't check discard it and declare no solution.

mertsj · Answer

Did your teacher teach you that you must always check a solution that comes from a radical equation because sometimes the squaring process introduces an extraneous root.

anonymous · Answer

No?

mertsj · Answer

So now you have been taught.  Always check the answers to radical equations.  Sometimes they will not check.

anonymous · Answer

Okay