Solve $LaTeX: \displaystyle x^{2} - 8 x - 9=0$

Since $LaTeX: \displaystyle a=1$ we need to find factors of $LaTeX: \displaystyle -9$ that add up to $LaTeX: \displaystyle -8$ . The factors are $LaTeX: \displaystyle -9$ and $LaTeX: \displaystyle 1$ . This gives $LaTeX: \displaystyle (x - 9)(x + 1)=0$ . The solutions are $LaTeX: \displaystyle x = 9$ and $LaTeX: \displaystyle x = -1$