# Solve the equation for x .

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• Dec 30th 2012, 12:40 AM
Arka
Solve the equation for x .
Can anyone help me in solving this equation ?? I found it in the chapter of Quadratic equations.....but I have failed to solve it with the methods I know ....Can anyone please help ?

$x = \sqrt{a-\sqrt{a+x}}$
• Dec 30th 2012, 01:10 AM
earboth
Re: Solve the equation for x .
Quote:

Originally Posted by Arka
Can anyone help me in solving this equation ?? I found it in the chapter of Quadratic equations.....but I have failed to solve it with the methods I know ....Can anyone please help ?

$x = \sqrt{a-\sqrt{a+x}}$

1. The general way to solve equations with square-roots is:

square - isolate remaining square-roots on one side - square - isolate remaining square-roots on one side - square - isolate remaining square-roots on one side - square .... until there is no square-root left.

2. You'll get finally a quadratic equation in a. Solve for a.

3. Afterwards solve these 2 equations for x.

4. Since you may transform a false equation into a true one by squaring you must check if your results satisfy the given original equation.