Solution - Radical equations

Radical Equation entered :

     √t+3+√t+10 = 7

Step by step solution :

Step  1  :

Isolate a square root on the left hand side :

     Original equation
     √t+3+√t+10 = 7

     Isolate
     √t+3 = -√t+10+7

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√t+3)² = (-√t+10+7)²

     After squaring
     t+3 = t+10+49-14√t+10

Step  3  :

Get remaining radical by itself :

     Current equation
     t+3 = t+10+49-14√t+10

     Isolate radical on the left hand side
     14√t+10 = -t-3+t+10+49

      Tidy up
     14√t+10 = 56

Step  4  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (14√t+10)² = (56)²

     After squaring
     196t+1960 = 3136

Step  5  :

Solve the linear equation :

     Rearranged equation
      196t  -1176 = 0

     Add  1176  to both sides
      196t  = 1176

     Divide both sides by 196
     A possible solution is :
     t = 6

Step  6  :

Check that the solution is correct :

     Original equation, root isolated, after tidy up
     √t+3 = -√t+10+7

     Plug in 6 for  t 
      √(6)+3 = -√(6)+10+7

      Simplify
      √9 = 3
      Solution checks !!
     Solution is:
      t = 6

One solution was found :