Rearranging Equations for Solving Complex Algebraic Expressions

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To solve the equation x = 90 - sqrt(100+x^2) - sqrt(100+x), the first step is to isolate one of the square root terms on one side. Squaring the equation will eliminate the square root, but this process may need to be repeated to fully simplify the expression. It's important to be cautious, as squaring twice could lead to a fourth-order polynomial. The quadratic formula may be applicable after the initial squaring, depending on the resulting equation. Following these steps should help in finding the value of x.
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Hopefully this can be done. It should be relatively simple, I'm just awful at rearranging equations.

I have: x = 90 - sqrt(100+x^2) - sqrt(100+x)

I want to find the value of x.

If someone could guide me through the process I would be eternally grateful. I know there's something about reversing operations, but I get lost in the details. ;)
 
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Jeebuz said:
Hopefully this can be done. It should be relatively simple, I'm just awful at rearranging equations.

I have: x = 90 - sqrt(100+x^2) - sqrt(100+x)

I want to find the value of b.

If someone could guide me through the process I would be eternally grateful. I know there's something about reversing operations, but I get lost in the details. ;)

I'm sorry, but I don't see any "b" in the equation.
 
cyby said:
I'm sorry, but I don't see any "b" in the equation.
Oops... so sorry. I meant x. I changed it at the last minute. :hangs head in shame:
 
Have you considered squaring the equation and then using the quadratic formula?
 
cyby said:
Have you considered squaring the equation and then using the quadratic formula?


Yeah,a geberal advice...But first,he mustput one (either one) of his square roots in the other side of the equation (left,if I'm not mistaking) and then square.He has to square 2 times in all,of course.Let's hope that by squaring twice he won't be gettin'a nasty 4-th order algebraic equation...
 

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