x-2^x+5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Sum and product of roots
[src]
/-log(2) \
W|--------|
\ 32 /
3 + -5 - -----------
log(2)
$$\left(-5 - \frac{W\left(- \frac{\log{\left(2 \right)}}{32}\right)}{\log{\left(2 \right)}}\right) + 3$$
/-log(2) \
W|--------|
\ 32 /
-2 - -----------
log(2)
$$-2 - \frac{W\left(- \frac{\log{\left(2 \right)}}{32}\right)}{\log{\left(2 \right)}}$$
/ /-log(2) \\
| W|--------||
| \ 32 /|
3*|-5 - -----------|
\ log(2) /
$$3 \left(-5 - \frac{W\left(- \frac{\log{\left(2 \right)}}{32}\right)}{\log{\left(2 \right)}}\right)$$
/-log(2) \
3*W|--------|
\ 32 /
-15 - -------------
log(2)
$$-15 - \frac{3 W\left(- \frac{\log{\left(2 \right)}}{32}\right)}{\log{\left(2 \right)}}$$
-15 - 3*LambertW(-log(2)/32)/log(2)
$$x_{1} = 3$$
/-log(2) \
W|--------|
\ 32 /
x2 = -5 - -----------
log(2)
$$x_{2} = -5 - \frac{W\left(- \frac{\log{\left(2 \right)}}{32}\right)}{\log{\left(2 \right)}}$$
x2 = -5 - LambertW(-log(2)/32)/log(2)