# 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

Algebra ->  Square-cubic-other-roots -> 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       Log On

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.

Found 2 solutions by Fombitz, jim_thompson5910:
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.

You can put this solution on YOUR website!

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

Multiply 3 by

Multiply

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}