Solution - Radical equations

Radical Equation entered :

     2√8x+20 = x

Step by step solution :

Step  1  :

Isolate the square root on the left hand side :

     Radical already isolated
     2√8x+20 = x

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (2√8x+20)² = (x)²

     After squaring
     32x+80 = x²

Step  3  :

Solve the quadratic equation :

     Rearranged equation
     x²  - 32x  -80 = 0

     This equation has two real roots:
       x1 = ( 32 + sqrt(1344) ) / 2 = 34.3303
      x2 = ( 32 - sqrt(1344) ) / 2 = -2.3303

Step  4  :

Check that the first solution is correct :

     Original equation
     2√8x+20 = x

     Plug in 34.3303 for  x 
      2√8•(34.3303) +20 = (34.3303)

      Simplify
      2√294.642 = 34.33
      Solution checks !!
     Solution is:
      x = 34.3303

Step  5  :

Check that the second solution is correct :

     Original equation
     2√8x+20 = x

     Plug in -2.3303 for  x 
      2√8•(-2.3303) +20 = (-2.3303)

      Simplify
      2√1.358 = -2.33
      Solution does not check
      2.33 ≠ -2.33 

One solution was found :