Question

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

Answer 1

D

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 = (12± √(144 - 28) )/(2)`

`x = (12± √(116) )/(2)`

`x = (12± √(4(29)) )/(2)`

`x = (12±( √(4))( √(29) ))/(2)`

`x = (12±2 √(29) )/(2)`

`x = 6± √(29)`

`∴x = 6 + √(29) \: \: \: or \: \: \:x = 6 - √(29)`