Question

Solve each quadratic equation by completing the square

Answer 1

x^2+2x-7=0

Answer 2

-x^2+6x+10=0

Answer 3

\[x^2+2x-7=0\]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
\[x=-1\pm\sqrt{8}\]

Answer 4

you can rewrite in simplest radical form as
\[x=-1\pm2\sqrt{2}\]

Answer 5

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
\[x=3\pm\sqrt{46}\]