Given:
[tex]3(x-9)^2=21[/tex]
Simplify:
[tex]3x^2-54x+222=0[/tex]
Use the quadratic formula to solve for the values of x.
a = 3
b = -54
c = 222
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]x=\frac{-(-54)\pm\sqrt[]{(-54)^2-4(3)(222)}}{2(3)}[/tex][tex]x=\frac{54\pm\sqrt[]{2916-2664}}{6}[/tex][tex]x=\frac{54\pm\sqrt[]{252}}{6}[/tex]
Solve for x (1)
[tex]x=\frac{54+\sqrt[]{252}}{6}[/tex][tex]x=\frac{54}{6}+\frac{6\sqrt[]{7}}{6}[/tex][tex]x=9+\sqrt[]{7}[/tex]
Solve for x (2)
[tex]x=\frac{54-\sqrt[]{252}}{6}[/tex][tex]x=\frac{54}{6}-\frac{6\sqrt[]{7}}{6}[/tex][tex]x=9-\sqrt[]{7}[/tex]
Therefore, the answer would be C.
[tex]x=9\pm\sqrt[]{7}[/tex]
