Solve the quadratic equation $\;$ $2x^2 - 5x - 10 = 0$ $\;$ giving your answer correct to two decimal places.
Given quadratic equation is $\;$ $2x^2 - 5x - 10 = 0$
Comparing with the standard quadratic equation $\;$ $ax^2 + bx + c = 0$ $\;$ gives
$a = 2$, $\;$ $b = -5$, $\;$ $c = -10$
Solution of the standard quadratic equation is $\;$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
$\therefore \;$ Solution of the given quadratic equation is
$\begin{aligned}
x & = \dfrac{5 \pm \sqrt{5^2 - 4 \times 2 \times \left(-10\right)}}{2 \times 2} \\\\
& = \dfrac{5 \pm \sqrt{25 + 80}}{4} \\\\
& = \dfrac{5 \pm \sqrt{105}}{4} \\\\
& = \dfrac{5 \pm 10.247}{4} \\\\
& = \dfrac{15.247}{4} \;\;\; or \;\;\; \dfrac{-5.247}{4} \\\\
& = 3.812 \;\;\; or \;\;\; -1.312
\end{aligned}$
i.e. $\;$ $x = 3.81$ $\;$ or $\;$ $x = -1.31$ $\;\;\;$ [correct to two decimal places]