Question

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answer 1

Answer:

D

Step-by-step explanation:

For a quadratic equation ax² +bx +c= 0, the quadratic formula is as below:

$\boxed{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }$

x² -12x +7= 0

$x = \frac{ - ( - 12)± \sqrt{( - 12) {}^{2} - 4(1)(7) } }{2(1)}$

$x = \frac{12± \sqrt{144 - 28} }{2}$

$x = \frac{12± \sqrt{116} }{2}$

$x = \frac{12± \sqrt{4(29)} }{2}$

$x = \frac{12±( \sqrt{4})( \sqrt{29} )}{2}$

$x = \frac{12±2 \sqrt{29} }{2}$

$x = 6± \sqrt{29}$

$∴x = 6 + \sqrt{29} \: \: \: or \: \: \:x = 6 - \sqrt{29}$