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)

Question 78900: I need help on solving this, please and thanks!! =)

So far I have this:
I rid the equation of roots by squaring both sides-

Simplified-

Combined like terms-

Divided both sides by x-

Solved for x-

But, when I plug that in to the original equation it comes out to be-

What am I doing wrong?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll start off where you went wrong
.....
Divided both sides by x-

You would actually get

So that wouldn't help at all since we have x in the denominator
--------------------------------------------------------------
Lets get 9x to the right side like this

Now factor

Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)

In order to factor , 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: substitute 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 again

So we now have

or
or
So our possible solutions are
or
However we must check these answers first

Check:
Plug in x=1

Since this is not true, we must discard the solution of x=1

Plug in x=8

works. This is our only solution
So our only solution is
x=8

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