Question

Solve. 3x2 = 33x + 24.

I need the exact quadratic formula answer and work thanks.

Answer 1

\[\Large 3x^2 = 33x + 24\]


\[\Large 3x^2 - 33x - 24 = 0\]


Now use the quadratic formula to solve


\[\Large x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\]


\[\Large x = \frac{-(-33)\pm\sqrt{(-33)^2-4(3)(-24)}}{2(3)}\]


\[\Large x = \frac{33\pm\sqrt{1089-(-288)}}{6}\]


\[\Large x = \frac{33\pm\sqrt{1377}}{6}\]


\[\Large x = \frac{33+\sqrt{1377}}{6} \ \text{or} \ x = \frac{33-\sqrt{1377}}{6}\]


\[\Large x = \frac{33+9\sqrt{17}}{6} \ \text{or} \ x = \frac{33-9\sqrt{17}}{6}\]


\[\Large x = \frac{11+3\sqrt{17}}{2} \ \text{or} \ x = \frac{11-3\sqrt{17}}{2}\]

Answer 2

thats what i got but these are the answers the question gives you...

Answer 3

For some odd reason, they didn't fully simplify the radical term. I'm not sure why.


In any event, the answer is choice A because sqrt(1377) = 3*sqrt(153) and this '3' will cancel.