abiboo 3 years ago Solve each quadratic equation by completing the square

1. abiboo

x^2+2x-7=0

2. abiboo

-x^2+6x+10=0

3. 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 $x=-1\pm\sqrt{8}$

4. anonymous

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

5. 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 $x=3\pm\sqrt{46}$