Question

Solve : root 24-10x = 3-4x

Answer 1

Step-by-step explanation:

Step by step solution :

Step  1  :

Isolate the square root on the left hand side :

     Radical already isolated

     √24-10x = 3-4x

Step  2  :

Eliminate the radical on the left hand side :

     Raise both sides to the second power

     (√24-10x)2 = (3-4x)2

     After squaring

     24-10x = 16x2-24x+9

Step  3  :

Solve the quadratic equation :

     Rearranged equation

      16x2  - 14x  -15 = 0

     This equation has two rational roots:

       {x1, x2}={3/2,-5/8}

 

Step  4  :

Check that the first solution is correct :

     Original equation

     √24-10x = 3-4x

     Plug in (3/2) for  x 

      √24-10•(3/2) = 3-4•(3/2)

      Simplify

      √9 = -3

      Solution does not check

      3 ≠ -3 

Step  5  :

Check that the second solution is correct :

     Original equation

     √24-10x = 3-4x

     Plug in  -(5/8) for  x 

      √24-10•(-5/8) = 3-4•(-5/8)

      Simplify

      √30.25 = 5.5

      Solution checks !!

     Solution is:

      x =  -(5/8)

One solution was found :

                        x =  -(5/8)

Answer 2

Answer:

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Step-by-step explanation:

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