$$\sqrt{x+13}=x+1 ?$$

Question

tkhunny · Answer

Please note, first, that $x+13\ge 0$.  You tell me why.

anonymous · Answer

Becasue 13 and anything added to that is greater than 0

anonymous · Answer

?

tkhunny · Answer

Okay, that's not wrong, but why do we care and why did I mention it?

anonymous · Answer

Dont we need to figure a number to make both sides satisfied?

tkhunny · Answer

Yes we do.  If we pick a number less than -13, the left-hand side doesn't exist.  It is important to know this.  If the result of our algebra is x = -25, we can just throw it out.  That will not work.

Okay, now square both sides.

anonymous · Answer

$$x^{2}+26=x^{2}+2 ?$$

tkhunny · Answer

$\left(\sqrt{x+13}\right) = x+13$

I really do not know how you managed that previous response.

$(x+1)^{2} = x^{2} + 2x + 1$

I think you may have forgotten your algebra.

$x+13 = x^{2} + 2x + 1$

anonymous · Answer

Thanks, and yes thats why i am here...for HELP!

tkhunny · Answer

You should be learning the solution of radical equations.

You shoudl already have as tools the squaring of radicals and the squaring of binomials.  you are supposed to bring tools with you.  Learning everything all over again is not a good plan.

So, what solution have you managed?