Question

solve by factoring: x^4-12x^2= 64

Answer 1

The final solution is all the values that make (x+4)(x−4)(x2+4)=0x+4⁢x-4⁢x2+4=0 true.x=−4,4,2i,−2i

Answer 2

minus 64 from both sides
x⁴-12x²-64=0
hmm
what 2 numbers multiply to -64 and add to get -12
-16 and 4
(x²-16)(x²+4)=0
oh look a difference of 2 perfect squares
(x²-4²)(x²+4)=0
(x-4)(x+4)(x²+4)=0
set each to zero

x-4=0
x=4

x+4=0
x=-4

x²+4=0
x²=-4
if you have learend complex roots then
sqrt both sides to get
x=-2i or 2i



solutions are
x=-4, 4, 2i or -2i