SOLUTION: x-2*sqrt(x-3)=3 solve for zero... I subtract x from both sides which = -2*sqrt(x-3)=3-x then I divide by -2 from both sides sqrt(x-3)=(3-x)/-2 then to get rid of

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Question 104710: x-2*sqrt(x-3)=3
solve for zero...
I subtract x from both sides which =
-2*sqrt(x-3)=3-x
then I divide by -2 from both sides
sqrt(x-3)=(3-x)/-2
then to get rid of the "sqrt" ^2 on both sides
x-3=(9+x^2)/4
then I subtract "x" and add 3 to both sides to solve for zero.
0=(9+x^2)/4-x+3
then I find a common denominator of 4 and solve
0=(9+x^2)/4 -4x/4+12/4 which equals 0=(x^2-4x+21)/4
then I multiply 4/1 on both side the loose the denominator.
0=x^2-4x+21 which can not be factored, but my text book gives a solution set of {7,3}. I cant find were I went wrong, please help.
Please note, this question had already been answered but the link to the answer did not work so this is why I am re-submitting it. Thank you.
Found 2 solutions by Fombitz, jim_thompson5910:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Here's the step where you got on the wrong path.

You're missing a term.

Re-work and continue from there.
You're on the right track otherwise.
Post another question if you get stuck.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation


Subtract x from both sides


Divide both sides by -2



Square both sides


Now this is where you went wrong, when you square you need to foil it to get instead of


Foil the numerator and square the denominator


Add 3 to both sides


Multiply 3 by


Multiply


Add the fractions


Combine like terms


Multiply both sides by 4


Subtract 4x from both sides


Combine like terms

Rearrange the terms


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic





the general solution using the quadratic equation is:







So lets solve ( notice , , and )





Plug in a=1, b=-10, and c=21




Negate -10 to get 10




Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because .)




Multiply to get




Combine like terms in the radicand (everything under the square root)




Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


or


Lets look at the first part:





Add the terms in the numerator

Divide


So one answer is






Now lets look at the second part:





Subtract the terms in the numerator

Divide


So another answer is




So our solutions are:

or





So this means the solution set is {7,3}
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