SOLUTION: Solve qudratic equation. (x^2-7)^2+3(x^2-7)+2=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve qudratic equation. (x^2-7)^2+3(x^2-7)+2=0      Log On


   

Question 237819: Solve qudratic equation.
(x^2-7)^2+3(x^2-7)+2=0
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Use a substitution:

Let

Now the problem becomes



Which, more's the pity, does not factor.

Use the quadratic formula:



(Verification left as an exercise for the student)

But now we have to go back and unwind the substitution:

Since ,







Yes, that is uglier than a mud fence. Notice that you actually have four roots. This is, of course, to be expected because this equation began life as a quartic not a quadratic.

John