Question

Solve the following equation and calculate the answer correct to two decimal places.
$x^2-5x-10=0$.

Answer 1

Given: $x^2-5x-10=0$

On comparing the given equation with $a{x}^2+bx+c=0$, we get:

$a=1,b=-5$ and $c=-10$

For $a{x}^2+bx+c=0$, we know that,

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ [Quadratic formula]

$\therefore x=\frac{5\pm \sqrt{(-5{)}^2-4\times 1\times (-10)}}{2\times 1}=\frac{5\pm \sqrt{65}}{2}$

$\Rightarrow \frac{5\pm 8.06}{2}$

$\Rightarrow \frac{5+8.06}{2},\frac{5-8.06}{2}$

$\Rightarrow \frac{13.06}{2},-\frac{3.06}{2}$

Hence, $x=6.53,\text{or}x=-1.53$.