Quadratic Equation by Factorization

Example 1

$$\textup{Solve } 4x^2-9=0$$

Solution

\begin{align*} 4x^2-9 & = 0\\ (2x)^2-(3)^2 & = 0\\ (2x+3)(2x-3) & = 0\\\\ 2x+3=0, \,\,\,\, & 2x-3=0\\ 2x=-3, \,\,\,\, & 2x=3\\ x=-\frac{3}{2}, \,\,\,\, & x=\frac{3}{2}\\ x=-1\frac{1}{2}, \,\,\,\, & x=1\frac{1}{2}\\ \end{align*}

Example 2

$$\textup{Solve } 25x^2-36=0$$

Solution

\begin{align*} 25x^2-36 & = 0\\ (5x)^2-(6)^2 & = 0\\ (5x+6)(5x-6) & = 0\\\\ 5x+6=0, \,\,\,\, & 5x-6=0\\ 5x=-6, \,\,\,\, & 5x=6\\ x=-\frac{6}{5}, \,\,\,\, & x=\frac{6}{5}\\ x=-1\frac{1}{5}, \,\,\,\, & x=1\frac{1}{5}\\ \end{align*}

Example 3

$$\textup{Solve } x^2+4x=0$$

Solution

\begin{align*} x^2+4x & = 0\\ x(x+4) & = 0\\\\ x=0, \,\,\,\, & x+4=0\\ & x=0-4\\ & x=-4\\ \end{align*}