Question 1170561
equation is x^2 + 16 = 0
subtract 16 from both sides of the equqtion to get:
x^2 = -16
solve for x to get:|
x = plus or minus sqrt(-16)
sqrt(-16) = sqrt(16*-1) = 4*sqrt(-1) = = 4i
x = plus or minus 4i.


that should be your answer.
to confirm, replace x with plus or minus 4i in the original equation to get:


when x = 4i,the equation becomes (4i)^2 + 16 = 0.
(4i)^2 becomes 4^2 * i^2 = 16 * -1 = -16.
equation becomes -16 + 16 = 0, which is true, confirming x = 4i is a solution.


when x = -4i, the equation becomes (-4i)^2 + 16 = 0
(-4i)^2 becomes (-1)^2 * 4^2 * i^2 = 1 * 16 * -1 = -16.
equation becomes -16 + 16 = 0, which is true, confirming x = -4i is also a solution.


the solution is x = plus or minus 4i.