VKV met breuken of rekenwerk

Gebruik de discriminant om volgende vierkantsvergelijkingen op te lossen

\(\frac{13}{4}x=-\frac{1}{2}x^2-\frac{9}{2}\)

\(\frac{13}{4}x=-\frac{1}{2}x^2-\frac{9}{2} \\ \Leftrightarrow \frac{1}{2}x^2+\frac{13}{4}x+\frac{9}{2}=0 \\ \Leftrightarrow \color{red}{4.} \left(\frac{1}{2}x^2+\frac{13}{4}x+\frac{9}{2}\right)=0 \color{red}{.4} \\ \Leftrightarrow 2x^2+13x+18=0 \\\text{We zoeken de oplossingen van } \color{blue}{2x^2+13x+18=0} \\ \\\begin{align} D & = b^2 - 4.a.c & & \\ & = (13)^2-4.2.18 & &\\ & = 169-144 & & \\ & = 25 & & \\ \\ x_1 & = \frac{-b-\sqrt{D}}{2.a} & x_2 & = \frac{-b+\sqrt{D}}{2.a} \\ & = \frac{-13-\sqrt25}{2.2} & & = \frac{-13+\sqrt25}{2.2} \\ & = \frac{-18}{4} & & = \frac{-8}{4} \\ & = \frac{-9}{2} & & = -2 \\ \\ V &= \Big\{ \frac{-9}{2} ; -2 \Big\} & &\end{align} \\ -----------------\)