Find the solution(s): sqrtx+9+sqrtx=9

Question

anonymous · Answer

I saw your name and had no choice but to answer this now...to bad I don't understand the question :s

anonymous · Answer

Heh

solomonzelman · Answer

$$\sqrt{x+9}+\sqrt{x}=9$$right?

anonymous · Answer

Yes

solomonzelman · Answer

square both sides,
using $$(a+b)^2=a^2+2ab+b^2$$for the left side,$$(x+9)+(2 \times \sqrt{x+9} \times \sqrt{x})+x=81$$

solomonzelman · Answer

$$2x+9+2\sqrt{x^2+9x}=81$$

solomonzelman · Answer

$$2\sqrt{x^2+9x}=-2x-9+81$$$$2\sqrt{x^2+9x}=-2x+72$$$$2~~(\sqrt{x^2+9x})=2~~(-x+36)$$$$\sqrt{x^2+9x}=-x+36$$

solomonzelman · Answer

square both sides,$$x^2+9x=x^2-72x+1296$$$$81x=1296$$$$x=16$$

anonymous · Answer

Wow

anonymous · Answer

The reason why I'm confused with this is because my teacher taught it to me differently and I don't get how she got the answer. Can I show you the way she did it?

solomonzelman · Answer

sure.

solomonzelman · Answer

I'll be back in short...

anonymous · Answer

Ok

anonymous · Answer

The first thing she did was she subtracted sqrtx from the left side. Then she squared each side to get rid of the radical and I get x+9 = 81-x. Then I subtract 9 from both sides and add x to both sides and then divide both sides by 2 and get 36 but I already know that's the wrong answer.

solomonzelman · Answer

$$(9-\sqrt{x})^2~~~????????$$What a poor teacher, she forgot about the middle term.

solomonzelman · Answer

Even a 16 year old like me knows this, common teacher.....

anonymous · Answer

brb one sec