Solution - Radical equations

Radical Equation entered :

     √8x-44 = x-7

Step by step solution :

Step  1  :

Isolate the square root on the left hand side :

     Radical already isolated
     √8x-44 = x-7

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√8x-44)² = (x-7)²

     After squaring
     8x-44 = x²-14x+49

Step  3  :

Solve the quadratic equation :

     Rearranged equation
     x²  - 22x  + 93 = 0

     This equation has two real roots:
       x1 = ( 22 + sqrt(112) ) / 2 = 16.2915
      x2 = ( 22 - sqrt(112) ) / 2 = 5.7085

Step  4  :

Check that the first solution is correct :

     Original equation
     √8x-44 = x-7

     Plug in 16.2915 for  x 
      √8•(16.2915) -44 = (16.2915) -7

      Simplify
      √86.332 = 9.292
      Solution checks !!
     Solution is:
      x = 16.2915

Step  5  :

Check that the second solution is correct :

     Original equation
     √8x-44 = x-7

     Plug in 5.7085 for  x 
      √8•( 5.7085) -44 = ( 5.7085) -7

      Simplify
      √1.668 = -1.292
      Solution does not check
      1.292 ≠ -1.292 

One solution was found :