Answer:
[tex]\large\boxed{x=-\dfrac{11}{12}\ \vee\ x=\dfrac{5}{12}}[/tex]
Step-by-step explanation:
[tex]x^2+\dfrac{1}{2}x+\dfrac{1}{16}=\dfrac{4}{9}\\\\x^2+2(x)\left(\dfrac{1}{4}\right)+\left(\dfrac{1}{4}\right)^2=\dfrac{4}{9}\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\\left(x+\dfrac{1}{4}\right)^2=\dfrac{4}{9}\iff x+\dfrac{1}{4}=\pm\sqrt{\dfrac{4}{9}}\\\\x+\dfrac{1}{4}=-\dfrac{2}{3}\ \vee\ x+\dfrac{1}{4}=\dfrac{2}{3}\qquad\text{multiply each sides by}\ (3)(4)=12[/tex]
[tex]12x+12\!\!\!\!\!\diagup^3\cdot\dfrac{1}{4\!\!\!\!\diagup_1}=12\!\!\!\!\!\diagup^4\cdot\left(-\dfrac{2}{3\!\!\!\!\diagup_1}\right)\ \vee\ 12x+12\!\!\!\!\!\diagup^3\cdot\dfrac{1}{4\!\!\!\!\diagup_1}=12\!\!\!\!\!\diagup^4\cdot\left(\dfrac{2}{3\!\!\!\!\diagup_1}\right)\\\\12x+3=-8\ \vee\ 12x+3=8\qquad\text{subtract 3 from each sides}\\\\12x=-11\ \vee\ 12x=5\qquad\text{divide each sides by 12}\\\\x=-\dfrac{11}{12}\ \vee\ x=\dfrac{5}{12}[/tex]
