anonymous
  • anonymous
I need someone to explain this lesson to me. Be patient while I write the problem.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Ok so it is walking me through the steps to solve for x \[\sqrt{x+21}-3=\sqrt{x}\]
anonymous
  • anonymous
Here are the steps:\[\sqrt{x+21}=3+\sqrt{x}\] \[x+21=9+6\sqrt{x}+x\] \[12=6\sqrt{x}\] \[\sqrt{x}=2\] \[x=4\]
anonymous
  • anonymous
The 2nd step is the one I didn't understand?\[x+21=9+6\sqrt{x}+x\]

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UsukiDoll
  • UsukiDoll
ahhhh... they squared both sides.
UsukiDoll
  • UsukiDoll
because we want x... no x^2 stuff square root of x just x so we square both sides \[(\sqrt{x+21})^2=(3+\sqrt{x})^2\]
anonymous
  • anonymous
Ok but wouldn't that leave us with \[x+21=9+x\]
UsukiDoll
  • UsukiDoll
the left side is correct.. the right one requires expansion
UsukiDoll
  • UsukiDoll
\[(\sqrt{x+21})(\sqrt{x+21}) = (3+\sqrt{x})(3+\sqrt{x})\]
UsukiDoll
  • UsukiDoll
so square root x square root is just whatever is in the square root so x+21 = (use foil method )
anonymous
  • anonymous
Ohhh Ok I get it thank you because the OI of FOIL add together to get the \[6\sqrt{x}\] thank you
UsukiDoll
  • UsukiDoll
yup
UsukiDoll
  • UsukiDoll
then what they did was shift that x to the left to eliminate it and the 9 is shifted to the left
UsukiDoll
  • UsukiDoll
then divide both sides by 6 afterwards square both sides again and x = 4
anonymous
  • anonymous
Yeah I get it thanks I am really liking this site it's helpin me out a lot

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