Question

Solve the quadratic equation by completing the square. x^2+8x-4=0

Answer 1

do you know how to "complete a square"?
first add \(4\) to both sides and start with
\[x^2+8x=4\] now what is half of \(8\)?

Answer 2

4

Answer 3

ok good, so we write
\[(x+4)^2=4+?\]now what is \(4^2\) ?

Answer 4

16

Answer 5

then that is what goes on the right side
\[(x+4)^2=4+16\\
(x+4)^2=20\]

Answer 6

now take the square root, don't forget the \(\pm\) and write
\[x+4=\pm\sqrt{20}\\x+4=\pm2\sqrt5\]

Answer 7

and finally subtract \(4\) from both sides and get
\[x=-4\pm2\sqrt5\] now it is done

Answer 8

ThankYou satellite73 !