SOLUTION: <pre> solve the radical equation. if there is no real solution, chose no solution 3x = &#8730;<span style="text-decoration: overline">20 - 3x</span></pre>

Algebra ->  Radicals -> SOLUTION: <pre> solve the radical equation. if there is no real solution, chose no solution 3x = &#8730;<span style="text-decoration: overline">20 - 3x</span></pre>       Log On


   

Question 754279: 
solve the radical equation. if there is no real solution, chose no solution 
3x = √20 - 3x
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

              3x = √20 - 3x

Square both sides of the equation:

           (3x)² = (√20 - 3x)²
 
            3²x² = 20 - 3x

             9x² = 20 - 3x

   9x² + 3x - 20 = 0

(3x - 4)(3x + 5) = 0

Use the zero-factor principle:

3x - 4 = 0;  3x + 5 = 0
    3x = 4;      3x = -5
     x = 4%2F3;      x = %28-5%29%2F3      
                  x = -5%2F3

We must check radical equations to see if answers 
are solutions or extraneous answers:

Checking x = 4%2F3 in original equation:

3%284%2F3%29=sqrt%2820-3%284%2F3%29%29
cross%283%29%284%2Fcross%283%29%29=sqrt%2820-cross%283%29%284%2Fcross%283%29%29%29
4=sqrt%2820-4%29
4=sqrt%2816%29
4=4

So 4%2F3 is a solution.

Checking x = -5%2F3 in original equation:

3%28-5%2F3%29=sqrt%2820-3%28-5%2F3%29%29
cross%283%29%28-5%2Fcross%283%29%29=sqrt%2820-cross%283%29%28-5%2Fcross%283%29%29%29
-5=sqrt%2820-%28-5%29%29
-5=sqrt%2820%2B5%29%29
-5=sqrt%2825%29
-5=5

So -5%2F3 is not a solution, but an extraneous answer.

Therefore the only solution is 4%2F3.

Edwin