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Solution - Radical equations

x=2
x=2

Other Ways to Solve

Radical equations

Step by Step Solution

Radical Equation entered :

     √8x-15 = 3-x

Step by step solution :

Step  1  :

Isolate the square root on the left hand side :

     Radical already isolated
     √8x-15 = 3-x

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√8x-15)2 = (3-x)2

     After squaring
     8x-15 = x2-6x+9

Step  3  :

Solve the quadratic equation :

     Rearranged equation
     x2  - 14x  + 24 = 0

     This equation has two rational roots:
       {x1, x2}={12, 2}
 

Step  4  :

Check that the first solution is correct :

     Original equation
     √8x-15 = 3-x

     Plug in 12 for  x 
      √8•(12)-15 = 3-(12)

      Simplify
      √81 = -9
 
     Solution does not check
      9 ≠ -9 

Step  5  :

Check that the second solution is correct :

     Original equation
     √8x-15 = 3-x

     Plug in 2 for  x 
      √8•(2)-15 = 3-(2)

      Simplify
      √1 = 1
 
     Solution checks !!
     Solution is:
      x = 2

One solution was found :

                        x = 2

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