Answer:
D
Step-by-step explanation:
For a quadratic equation ax² +bx +c= 0, the quadratic formula is as below:
[tex]\boxed{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }[/tex]
x² -12x +7= 0
[tex]x = \frac{ - ( - 12)± \sqrt{( - 12) {}^{2} - 4(1)(7) } }{2(1)} [/tex]
[tex]x = \frac{12± \sqrt{144 - 28} }{2} [/tex]
[tex]x = \frac{12± \sqrt{116} }{2} [/tex]
[tex]x = \frac{12± \sqrt{4(29)} }{2} [/tex]
[tex]x = \frac{12±( \sqrt{4})( \sqrt{29} )}{2} [/tex]
[tex]x = \frac{12±2 \sqrt{29} }{2} [/tex]
[tex]x = 6± \sqrt{29} [/tex]
[tex]∴x = 6 + \sqrt{29} \: \: \: or \: \: \:x = 6 - \sqrt{29}[/tex]
