(-1/2)n=-36

Solution for (-1/2)n=-36 equation:

(-1/2)n=-36

We move all terms to the left:

(-1/2)n-(-36)=0


Domain of the equation: 2)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(-1/2)n+36=0

We multiply parentheses

-1n^2+36=0

a = -1; b = 0; c = +36;
Δ = b2-4ac
Δ = 02-4·(-1)·36
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-1}=\frac{-12}{-2}
=+6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-1}=\frac{12}{-2}
=-6
$