Question

solve by completing the square. 8x^2+22x=21

Answer 1

divide by 8 to get
\[x^2+\frac{11}{4}x=\frac{21}{8}\] then
\[(x+\frac{11}{8})^2=\frac{21}{8}+\frac{121}{64}\]
\[(x+\frac{11}{8})^2=\frac{289}{64}\]
\[x+\frac{11}{8}=\pm\sqrt{\frac{289}{64}}\]
\[x+\frac{11}{8}=\pm\frac{17}{8}\]

Answer 2

and so
\[x=\frac{17}{8}-\frac{11}{8}=\frac{6}{8}=\frac{3}{4}\] or
\[x=\frac{-17}{8}-\frac{11}{8}=\frac{-28}{8}=-\frac{7}{2}\]