SOLUTION: How do I solve: {{{ sqrt( s+25 ) +5 = s}}} Thank you.

Question 336199: How do I solve:

Thank you.

Found 2 solutions by jim_thompson5910, galactus:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Subtract 5 from both sides.

Square both sides.

FOIL

Get every term to one side.

Combine like terms.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "s":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible solutions are or

However, if you plug in into the original equation, you'll get a contradiction. So is NOT a solution.

So the only true solution is

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my website.

Jim
Answer by galactus(183) (Show Source): You can put this solution on YOUR website!

Subtract 5 from both sides:

Square both sides to shed the radical:

Expand to form the quadratic:

Set to 0 by bringing everything to one side:

Factor out s:

Now, it is easy to see that the two solutions are s=0 and s=11.
But, one of these may be extraneous. Check to see if they work:
For s=0:
........clearly untrue.
Check s=11:
......clearly true.
s=11 is the solution we want.

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