How do you solve #4x ^ { 6} + 16x ^ { 4} - 25x ^ { 2} - 100= 0#?

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Answer 1 · 2017-12-05T19:17:56

Factor out #4x^4# from the first two terms and -25 from the last two

Split the equation into two parts, hoping to find a common internal expression

#4x^4(x^2+4)-25(x^2+4)=0#

The common internal expression is then #x^2+4#

Then combine to #(4x^4-25)(x^2+4)=0#

This means #4x^4-25=0# or #x^2+4=0#

#4x^4=25#

#x^4=25/4#
#x=+-(25/4)^(1/4)#

#x^2=-4#
#x= +-2i#