SOLUTION: What is the solution for x? sqrt(x+5)=x^2-5

Question 837887: What is the solution for x?
sqrt(x+5)=x^2-5
Answer by tommyt3rd(5050) (Show Source): You can put this solution on YOUR website!
The solution is very long a little tough...but I will summarize...

square both sides to get

Simplify and rewrite as

We wish to write this as a product of square polynomials, so after some careful thought and experimentation we use

When we expand this version and compare coefficients we can determine that

1)
2)
3)

This nonlinear can be solved by substitution. It has a rational solution of

therefore we can write:

and that means

so that

and we know there are only two solutions so...

RELATED QUESTIONS
1.) The solution to sqrt 2x+3 - sqrt x-1=1 is x=3? true or false 2.) The solution to... (answered by ikleyn)

What is the extraneous solution of sqrt(x-3)= (x-5) also sqrt... (answered by jsmallt9)

What are the extraneous solutions and the steps for:... (answered by Alan3354)

The solution for the equation, {{{ x+4 = sqrt (x^3-2x^2-5)+3 }}}, to the nearest... (answered by Fombitz,josgarithmetic)

what is the solution set for x^2- 12x=-5 (answered by ewatrrr)

find the exact solution for [5]-1/x=[5]/2 [] means sqrt / means... (answered by shantalboodram)

1. Find an exact solution for sqrt 5-1/x=sqrt 5/2. Then find the approximate solution to... (answered by Gogonati)

Please help he solve this equation {{{ sqrt(2x+5)=X-5 }}} I have to be able to fill (answered by Alan3354)

Use the given information to find cos(x/2), sin(x/2), and tan(x/2): tan x = 2, pi < x <... (answered by lwsshak3)