Question

Solve by the quadratic formula: m^2 -6m+4=0

Can you please show the steps.

Answer 1

The quadratic formula is:

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

In your equation:
$a=1$
$b=-6$
$c=4$

So now we just plug and chug:

$x= \frac{-(-6) \pm \sqrt{(-6)^2-4(1)(4)} }{2(1)}$

$x= \frac{6 \pm \sqrt{36-16} }{2}$

$x= \frac{6 \pm \sqrt{20} }{2}$

$x= \frac{6 \pm 2\sqrt{5} }{2}$

$x= 3\pm \sqrt{5} }$

So the two solutions are $x= 3 + \sqrt{5} }$ and $x= 3 - \sqrt{5} }$