SOLUTION: I need help on solving this, please and thanks!! =) {{{ sqrt(3x+1) = x-3 }}} So far I have this: I rid the equation of roots by squaring both sides- {{{ 3x+1 = (x-3)(x-3)

Algebra ->  Radicals -> SOLUTION: I need help on solving this, please and thanks!! =) {{{ sqrt(3x+1) = x-3 }}} So far I have this: I rid the equation of roots by squaring both sides- {{{ 3x+1 = (x-3)(x-3)      Log On


   

Question 78900: I need help on solving this, please and thanks!! =)
+sqrt%283x%2B1%29+=+x-3+
So far I have this:
I rid the equation of roots by squaring both sides-
+3x%2B1+=+%28x-3%29%28x-3%29+
Simplified-
+3x%2B1+=+x%5E2-6x%2B9+
Combined like terms-
+9x+=+x%5E2%2B8+
Divided both sides by x-
+9+=+x%2B8+
Solved for x-
+x+=+1+
But, when I plug that in to the original equation it comes out to be-
+2+=+-2+
What am I doing wrong?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll start off where you went wrong
.....
Divided both sides by x-
+9+=+x%2B8+
You would actually get
9=x%2B8%2Fx
So that wouldn't help at all since we have x in the denominator
--------------------------------------------------------------
Lets get 9x to the right side like this

+0=+x%5E2-9x%2B8+
Now factor
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor 1%2Ax%5E2%2B-9%2Ax%2B8, first we need to ask ourselves: What two numbers multiply to 8 and add to -9? Lets find out by listing all of the possible factors of 8


Factors:

1,2,4,8,

-1,-2,-4,-8,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 8.

1*8=8

2*4=8

(-1)*(-8)=8

(-2)*(-4)=8

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -9

||||
First Number|Second Number|Sum
1|8|1+8=9
2|4|2+4=6
-1|-8|-1+(-8)=-9
-2|-4|-2+(-4)=-6
We can see from the table that -1 and -8 add to -9.So the two numbers that multiply to 8 and add to -9 are: -1 and -8 Now we substitute these numbers into a and b of the general equation of a product of linear factors which is: %28x%2Ba%29%28x%2Bb%29substitute a=-1 and b=-8 So the equation becomes: (x-1)(x-8) Notice that if we foil (x-1)(x-8) we get the quadratic 1%2Ax%5E2%2B-9%2Ax%2B8 again


So we now have
%28x-1%29%28x-8%29=0
x-1=0 or x-8=0
x=1 or x=8
So our possible solutions are
x=1 or x=8
However we must check these answers first

Check:
Plug in x=1
+sqrt%283%281%29%2B1%29+=+1-3+
2=-2
Since this is not true, we must discard the solution of x=1

Plug in x=8
+sqrt%283%288%29%2B1%29+=+1-3+
+sqrt%2825%29+=+8-3+
+5+=+5+ works. This is our only solution
So our only solution is
x=8