# Which method do you use to solve the quadratic equation 81x^2+1=0?

Nov 3, 2014

I would try to isolate $x$.

$81 {x}^{2} + 1 = 0$

by subtracting 1,

$\implies 81 {x}^{2} = - 1$

by dividing by 81,

$\implies {x}^{2} = - \frac{1}{81}$

Since ${x}^{2}$ can never be negative for a real number $x$, the equation has no real solutions; however, if you are looking for its complex solutions, then by taking the square-root,

$\implies x = \pm \sqrt{- \frac{1}{81}} = \pm \frac{i}{9}$

I hope that this was helpful.