Solve the equation 2x 2 9x 5 using the completi... - SS2 Mathematics Simultaneous Linear and Quadratic Equations Question

\[{2x}^{2} + 9x = 5\]

\[x^{2} + \frac{9}{2}x = \frac{5}{2}\]

\[x^{2} + \frac{9}{2}x + {(\frac{9}{4})}^{2} = \frac{5}{2} + {(\frac{9}{4})}^{2}\]

\[x^{2} + \frac{9}{2}x + \frac{81}{16} = \frac{5}{2} + \frac{81}{16}\]

\[{(x + \frac{9}{4})}^{2} = \frac{5}{2} + \frac{81}{16}\]

\[{(x + \frac{9}{4})}^{2} = \frac{40 + 81}{16}\]

\[{(x + \frac{9}{4})}^{2} = \frac{121}{16}\]

\[x + \frac{9}{4} = \pm \sqrt{\frac{121}{16}} = \pm \frac{11}{4}\]

\[x = - \frac{9}{4} \pm \frac{11}{4}\]

\[x = - \frac{9}{4} + \frac{11}{4}\ \ \ \ \ or\ \ \ \ \ - \frac{9}{4} - \frac{11}{4}\]

\(x = \frac{11 - 9}{4}\ \ \ \ or\ \frac{- 9 - 11}{4}\)

\(x = \frac{1}{2}\) or \(- 5\)