How do you find the solution to the quadratic equation #2(x^2 - 5)^2 - 13 (x^2 - 5) + 20 = 0#?

1 Answer
Alan P.
May 1, 2015

Let #p=(x^2-5)#
and solve
#2p^2 - 13p +20 = 0#
Then for each solution (in terms of #p#)
solve for #x#

#2p^2 - 13p +20 = 0#
#rarr (p-4)(2p-5) = 0#
#rarr p=4 " or " p = 5/2#

If #p=4#
#x^2-5 = 4#
#rarr x=+3 " or " x=-3#

If #p=5/2#
#x^2-5 = 5/2#
#rarr x=+15/2 = +7 1/2 " or " x=-15/2 = -7 1/2#

So
#x epsilon {-7 1/2, -3, +3, +7 1/2}#

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