What is the solution for x in the given equation sqr rt 9x+7+sqr rt 2x=7?

 x=2

Step-by-step explanation:

Step by step solution :

Step  1  :

Isolate a square root on the left hand side :

    Original equation

    √9x+7+√2x = 7

    Isolate

    √9x+7 = -√2x+7

Step  2  :

Eliminate the radical on the left hand side :

    Raise both sides to the second power

    (√9x+7)2 = (-√2x+7)2

    After squaring

    9x+7 = 2x+49-14√2x

Step  3  :

Get remaining radical by itself :

    Current equation

    9x+7 = 2x+49-14√2x

    Isolate radical on the left hand side

    14√2x = -9x-7+2x+49

     Tidy up

    14√2x = -7x+42

Step  4  :

Eliminate the radical on the left hand side :

    Raise both sides to the second power

    (14√2x)2 = (-7x+42)2

    After squaring

    392x = 49x2-588x+1764

Step  5  :

Solve the quadratic equation :

    Rearranged equation

     49x2  - 980x  + 1764 = 0

    This equation has two rational roots:

      {x1, x2}={18, 2}

Step  6  :

Check that the first solution is correct :

    Original equation, root isolated, after tidy up

    √9x+7 = -√2x+7

    Plug in 18 for  x

     √9•(18)+7 = -√2•(18)+7

     Simplify

     √169 = 1

     Solution does not check

     13 ≠ 1

Step  7  :

Check that the second solution is correct :

    Original equation, root isolated, after tidy up

    √9x+7 = -√2x+7

    Plug in 2 for  x

     √9•(2)+7 = -√2•(2)+7

     Simplify

     √25 = 5

     Solution checks !!

    Solution is:

     x = Step by step solution :

Step  1  :

Isolate a square root on the left hand side :

    Original equation

    √9x+7+√2x = 7

    Isolate

    √9x+7 = -√2x+7

Step  2  :

Eliminate the radical on the left hand side :

    Raise both sides to the second power

    (√9x+7)2 = (-√2x+7)2

    After squaring

    9x+7 = 2x+49-14√2x

Step  3  :

Get remaining radical by itself :

    Current equation

    9x+7 = 2x+49-14√2x

    Isolate radical on the left hand side

    14√2x = -9x-7+2x+49

     Tidy up

    14√2x = -7x+42

Step  4  :

Eliminate the radical on the left hand side :

    Raise both sides to the second power

    (14√2x)2 = (-7x+42)2

    After squaring

    392x = 49x2-588x+1764

Step  5  :

Solve the quadratic equation :

    Rearranged equation

     49x2  - 980x  + 1764 = 0

    This equation has two rational roots:

      {x1, x2}={18, 2}

Step  6  :

Check that the first solution is correct :

    Original equation, root isolated, after tidy up

    √9x+7 = -√2x+7

    Plug in 18 for  x

     √9•(18)+7 = -√2•(18)+7

     Simplify

     √169 = 1

     Solution does not check

     13 ≠ 1

Step  7  :

Check that the second solution is correct :

    Original equation, root isolated, after tidy up

    √9x+7 = -√2x+7

    Plug in 2 for  x

     √9•(2)+7 = -√2•(2)+7

     Simplify

     √25 = 5

     Solution checks !!

    Solution is:

     x = 2

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step-by-step explanation: