Question

What are the exact solutions of x2 − 3x − 7 = 0?

Answer 1

$\bf ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-3}x\stackrel{\stackrel{c}{\downarrow }}{-7}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x=\cfrac{-(-3)\pm\sqrt{(-3)^2-4(1)(-7)}}{2(1)}\implies x=\cfrac{3\pm\sqrt{9+28}}{2}\implies x=\cfrac{3\pm\sqrt{37}}{2}$