Question

What is the the smaller of the solutions? x^2-7x+3=0

Answer 1

Factor
erm, nope

use quadraticc formula
for
0=ax²+bx+c

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

so

given
0=1x²-7x+3
a=1
b=-7
c=3

$x=\frac{-(-7)+/-\sqrt{(-7)^2-4(1)(3)}}{2(1)}$
$x=\frac{7+/-\sqrt{49-12}}{2}$
$x=\frac{7+/-\sqrt{37}}{2}$
$x=\frac{7+/-\sqrt{37}}{2}$

the solutions are $x=\frac{7+\sqrt{37}}{2}$ and $x=\frac{7-\sqrt{37}}{2}$

the smaller solution will be $x=\frac{7-\sqrt{37}}{2}$