Question

I need help solving this: x-7} = 5" alt="x- \sqrt{2x-7} = 5" align="absmiddle" class="latex-formula">

Answer 1

Hope this helps :).  

Answer 2

I am hoping this was explained well enough:

Step  1  :

Isolate the square root on the left hand side :

    Radical already isolated  

    √2x-7 = 5-x

Step  2  :

Eliminate the radical on the left hand side :

    Raise both sides to the second power

    (√2x-7)2 = (5-x)2

    After squaring  

    2x-7 = x2-10x+25

Step  3  :

Solve the quadratic equation :

    Rearranged equation

    x2  - 12x  + 32 = 0

    This equation has two rational roots:

      {x1, x2}={8, 4}

 

Step  4  :

Check that the first solution is correct :

    Original equation

    √2x-7 = 5-x

    Plug in 8 for  x  

     √2•(8)-7 = 5-(8)

     Simplify

     √9 = -3

     Solution does not check  

     3 ≠ -3  

Step  5  :

Check that the second solution is correct :

    Original equation

    √2x-7 = 5-x

    Plug in 4 for  x  

     √2•(4)-7 = 5-(4)

     Simplify

     √1 = 1

     Solution checks !!

    Solution is:  

     x = 4

One solution was found :

                       x = 4