Question

4xsquared - 9=0? could anyone help me solve this quadratic equation by FACTORING?

Answer 1

$\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\ 4x^2-9=0\implies 2^2x^2-3^2=0\implies (2x)^2-3^2=0 \\\\\\\ [(2x)-3][(2x)+3]=0\implies \begin{cases} 2x-3=0\\ 2x=3\\ x=\frac{3}{2}\\ ------\\ 2x+3=0\\ 2x=-3\\ x=-\frac{3}{2} \end{cases}$