Question

Directions: Solve equation by completing the square.
r^2-4r-91=7

Answer 1

\[r^2-4r-91=7\]

add 91

\[r^2-4r=98\]

take 1/2 of -4 and then square
[\frac{1}{2}\times(-4)=-2\]
\[(-2)^2=4\]

add 4 to both sides

\[r^2-4r+4=98+4\]

\[r^2-4r+4=102\]

now the left hand side factors

\[(r-2)^2=102\]

take square root of both sides

\[r-2=\pm\sqrt{102}\]

add 2

\[r=2\pm\sqrt{102}\]

Answer 2

let me know if you have any other problems

Answer 3

the part above that looks a little weird says

\[\frac{1}{2}\times(-4)=-2\]