Question

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

Answer 1

I would try to isolate `x`.

`81x^2+1=0`

by subtracting 1,

`=> 81x^2=-1`

by dividing by 81,

`=> x^2=-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,

`=> x=pmsqrt{-1/81}=pm i/9`

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I hope that this was helpful.