Is it possible to solve an equation such as $x^2+5^x - 10 = 0$ without using graphical methods? I tried using logarithms to find the answer to $x^2+5^x-10=0$ but I didn't have any luck. Is there a way of solving the above equation algebraically, or do you have to use a graphical method?

$x^2+5^x-10=0$
$x= ± \sqrt{10-5^x}$
$10-5^x=1, 4, 9$
$10-5^x=1$  ⇒ $x=\frac{log (9)}{log (5)}=1.36$
$10-5^x=4$  ⇒ $x=\frac{log (6)}{log (5)}=1.11$
$10-5^x=9$  ⇒ $x=\frac{log (1)}{log (5)}=0$
Non of these results satisfy the equation.But we can use try and error method.We can see that x must be between $1.36$ and $1.11$, we try $x=1.3$:
$1.3^2=1.69=1-5^x$  ⇒ $x=\frac{log 8.31}{log 5}≈1.3$
