Question 709890
To solve, let's first factor our expression:  x^4 + x^2 - 30.  What two numbers, when multiplied, give us -30, and when added, give us 1?  Let's find out:

-1 x 30 = -30; -1 + 30 = 29  NO


-2 x 15 = -30; -2 + 15 = 13  NO


-3 x 10 = -30; -3 + 10 = 7  NO


-5 x 6 = -30; -5 + 6 = 1  YES!!


Since -5 and 6 work, we will now factor our expression:


{{{x^2 - 5)(x^2 + 6)}}}


To find x, we will set each of these factors equal to 0:


x^2 - 5 = 0 =


Add 5 to both sides:


x^2 = 5


Finally, take the square root of both sides, remembering to add a +- sign.  This gives us 


{{{x = +-sqrt(5)}}}


Now, take our other factor and set to zero:


x^2 + 6 = 0


Subtract 6 from both sides, giving us


x^2 = -6


Take the square root of both sides, remembering to add a +- sign to the right side equation:


{{{x = +-sqrt(-6)}}}


Remember that since {{{i = sqrt(-1)}}}, {{{sqrt(-6) = i*sqrt(6)}}}


Our final answer is x = {{{sqrt(5)}}}, {{{-sqrt(5)}}}, {{{i*sqrt(6)}}}, and {{{-i*sqrt(6)}}}