Question

What is the solution to the equation below? √x-4=x-10

Answer 1

Answer:

$x=13$

Step-by-step explanation:

Step 1: Isolate the square root on the left hand side

 Radical already isolated

  √x-4 = x-10

Step 2: Eliminate the radical on the left hand side

Raise both sides to the second power

    (√x-4)2 = (x-10)2

    After squaring

    x-4 = x2-20x+100

Step 3: Solve the quadratic equation

    Rearranged equation

    x2  - 21x  + 104 = 0

    This equation has two rational roots:

      {x1, x2}={13, 8}

Step 4: Check that the first solution is correct

    Original equation

    √x-4 = x-10

    Plug in 13 for  x

     √(13)-4 = (13)-10

     Simplify

     √9 = 3

     Solution checks !!

    Solution is:

     x = 13

Step 5: Check that the second solution is correct

    Original equation

    √x-4 = x-10

    Plug in 8 for  x

     √(8)-4 = (8)-10

     Simplify

     √4 = -2

     Solution does not check

     2 ≠ -2

One solution was found :

     x = 13