Question

Solve using the quadratic formula:

Answer 1

Answer:

$\boxed{x_1 = \frac{7 + \sqrt{5} }{2} ~~or~~x_2 = \frac{7 - \sqrt{5} }{2} }$

Step-by-step explanation:

$x^2 - 7x + 11 = 0$

$x^2 - 7x = -11$

$(x - \frac{7}{2} )^2 - \frac{49}{4} = -11$

$(x - \frac{7}{2} )^2 = -11 + \frac{49}{4}$

$(x - \frac{7}{2} )^2 = \frac{5}{4}$

$x - \frac{7}{2} = \pm \sqrt{\frac{5}{4}}$

$x = \frac{7 \pm \sqrt{5} }{2}$