We have to solve this expression:
[tex](4x+3)^2=18[/tex]This can be expressed as a quadratic equation, so we will probably get two solutions.
We can start by writing:
[tex]\begin{gathered} (4x+3)^2=18 \\ 4x+3=\pm\sqrt{18} \\ 4x=-3\pm\sqrt{18} \\ x=\frac{-3\pm\sqrt{18}}{4} \end{gathered}[/tex]We can simplify it a little further as:
[tex]\begin{gathered} x=\frac{-3\pm\sqrt{18}}{4} \\ x=\frac{-3\pm\sqrt{9*2}}{4} \\ x=\frac{-3\pm3\sqrt{2}}{4} \\ x=\frac{3}{4}(1\pm\sqrt{2}) \\ =>x_1=\frac{3}{4}(1-\sqrt{2}) \\ =>x_2=\frac{3}{4}(1+\sqrt{2}) \end{gathered}[/tex]Answer: the solutions are 3/4*(1-√2) and 3/4*(1+√2).