Let's use the quadratic formula
[tex] \frac{ - b( + - ) \sqrt{ {b}^{2} - 4ac} }{4a} [/tex]
a = 1, b = 0, c = -18
[tex] \frac{ - (0)( + - ) \sqrt{ {(0)}^{2} - 4(1)( - 18)} } {4(1)} \\ \frac{( + - ) \sqrt{72} }{4} [/tex]
This is now split into two equations:
[tex] \frac{ + \sqrt{72} }{4}[/tex]
and
[tex] \frac{ - \sqrt{72} }{4} [/tex]
Since[tex] \frac{ \sqrt{72} }{4} \\ = \frac{6 \sqrt{2} }{4} \\ = \frac{3 \sqrt{2} }{2} [/tex]
The answer is
[tex] \frac{3 \sqrt{2} }{2} \: and \: \frac{ - 3 \sqrt{2} }{2} [/tex]
which means there are 2 real number solutions to the problem: answer B.
