anonymous
  • anonymous
Solve each quadratic equation by completing the square
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
x^2+2x-7=0
anonymous
  • anonymous
-x^2+6x+10=0
anonymous
  • anonymous
\[x^2+2x-7=0\]add 7 \[x^2+2x=7\] take half of 2, which is 1 and write \[(x+1)^2=7+1^2=8\] take the square root, don't forget the \(\pm\) and write \[x+1=\pm\sqrt{8}\] subtract 1 get \[x=-1\pm\sqrt{8}\]

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anonymous
  • anonymous
you can rewrite in simplest radical form as \[x=-1\pm2\sqrt{2}\]
anonymous
  • anonymous
second one is similar \[-x^2+6x+10=0\]start by multiplying by \(-1\) to get \[x^2-6x-10=0\] add 10 get \[x^2-6x=10\]half of \(-6\) is \(-3\) \[(x-3)^2=10+6^2=46\] take the square root \[x-3=\pm\sqrt{46}\] add 3 \[x=3\pm\sqrt{46}\]

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