Solve $LaTeX: \displaystyle 16 x^{2} - 49=0$

This is an ac method factoring. The factors of $LaTeX: \displaystyle ac = -784$ that add up to $LaTeX: \displaystyle 0$ are $LaTeX: \displaystyle -28$ and $LaTeX: \displaystyle 28$ . Separating gives $LaTeX: \displaystyle (16 x^{2} - 28 x)+(28 x - 49)=0$ . This gives $LaTeX: \displaystyle (4 x + 7)(4 x - 7)=0$ . The solutions are $LaTeX: \displaystyle x = - \frac{7}{4}$ and $LaTeX: \displaystyle x = \frac{7}{4}$