Solve $LaTeX: \displaystyle x^{2} - 10 x + 21=0$

Since $LaTeX: \displaystyle a=1$ we need to find factors of $LaTeX: \displaystyle 21$ that add up to $LaTeX: \displaystyle -10$ . The factors are $LaTeX: \displaystyle -3$ and $LaTeX: \displaystyle -7$ . This gives $LaTeX: \displaystyle (x - 3)(x - 7)=0$ . The solutions are $LaTeX: \displaystyle x = 3$ and $LaTeX: \displaystyle x = 7$