Question

Solve this equation by using the Quadratic Formula. r^2+25=0. Can someone explain to me why the answer is no solution or empty set?

Answer 1

because that equals:

r^2=-25

this means that r is an imaginary number.. so there is no answer.

Answer 2

well that's sort of two different things you said there madscientist
there is /no real number/ solution, there are only /imaginary/ solutions
hence the answer is not the empty set, but 'no real number'; though you may be excluding imaginary numbers at this point in your studies

Answer 3

the reason no real number satisfies\[r^2=25\]can be seen by trying the likely candidates for answers, 5 and -5:\[(5)^2=25\]\[(-5)^2=(-5)(-5)=25\]so since negative times negative is always positive, we find no number that squares to become negative among the 'real' numbers
(real numbers are basically what you probably just know as 'numbers')