Question

I need someone to explain this lesson to me. Be patient while I write the problem.

Answer 1

Ok so it is walking me through the steps to solve for x \[\sqrt{x+21}-3=\sqrt{x}\]

Answer 2

Here are the steps:\[\sqrt{x+21}=3+\sqrt{x}\] \[x+21=9+6\sqrt{x}+x\] \[12=6\sqrt{x}\] \[\sqrt{x}=2\] \[x=4\]

Answer 3

The 2nd step is the one I didn't understand?\[x+21=9+6\sqrt{x}+x\]

Answer 4

ahhhh... they squared both sides.

Answer 5

because we want x... no x^2 stuff square root of x
just x
so we square both sides
\[(\sqrt{x+21})^2=(3+\sqrt{x})^2\]

Answer 6

Ok but wouldn't that leave us with \[x+21=9+x\]

Answer 7

the left side is correct.. the right one requires expansion

Answer 8

\[(\sqrt{x+21})(\sqrt{x+21}) = (3+\sqrt{x})(3+\sqrt{x})\]

Answer 9

so square root x square root is just whatever is in the square root so
x+21 = (use foil method )

Answer 10

Ohhh Ok I get it thank you because the OI of FOIL add together to get the \[6\sqrt{x}\] thank you

Answer 11

yup

Answer 12

then what they did was shift that x to the left to eliminate it
and the 9 is shifted to the left

Answer 13

then divide both sides by 6
afterwards square both sides again and x = 4

Answer 14

Yeah I get it thanks I am really liking this site it's helpin me out a lot