(-10a⁴)+(-10a²)=-200
we can simplify this expression if we divide all terms by 10
-10a⁴-10a²=-200
-a⁴-a²=-20
a⁴+a²-20=0
a²=z
z²+z-20=0
Now, we solve this square equation:
z=[-1⁺₋√(1+80)]/2=(-1⁺₋9)/2
We have two solutions:
z₁=(-1-9)/2=-5
z₂=(-1+9)/2=4
a²=z
so:
a²=-5 ⇒a=⁺₋√-5 This solution is not valid.
a²=4 ⇒a=⁺₋√4
We have two solution:
a₁=-2
a₂=2
Answer: the value of a can be -2 or 2.