Question

Solve each of the following equations for x and give, in each case, your answer correct to 2 decimal places:

(v) $x^2-5x-10=0$

Answer 1

Compare $x^2-5x-10=0$ with $a{x}^2+bx+c=0$

$a=1,b=-5andc=-10$

We know that, for $a{x}^2+bx+c=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ are roots of the equation.

$\Rightarrow x=\frac{-(-5)\pm \sqrt{(-5{)}^2-4(1\left)\right(-10)}}{2\left(1\right)}$

$\Rightarrow x=\frac{5\pm \sqrt{25+40}}{2}$

$\Rightarrow x=\frac{5\pm \sqrt{65}}{2}$

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

$\Rightarrow x=\frac{5+8.06}{2}andx=\frac{5-8.06}{2}$

$\Rightarrow x=\frac{13.06}{2}andx=\frac{-3.06}{2}$

$\therefore x=6.53and-1.53$.