SOLUTION: Solve the equation by introducing a substitution that transforms this equation into quadratic form. x^4-35x^2+304=0 I'm not even sure how to begin this, but my paper has a sp

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Solve the equation by introducing a substitution that transforms this equation into quadratic form. x^4-35x^2+304=0 I'm not even sure how to begin this, but my paper has a sp      Log On


   

Question 903111: Solve the equation by introducing a substitution that transforms this equation into quadratic form.
x^4-35x^2+304=0
I'm not even sure how to begin this, but my paper has a spot for four answers if that helps?
Found 2 solutions by ewatrrr, josgarithmetic:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

x^4-35x^2+304=0

Let X = x^2

X^2 -35X + 304 = 0

(X-19)(X-16) = 0

X = 16, x = ± 4   (x = ±√X)

X = 19, x = ± √19

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Let some variable be x%5E2. Check the discriminant to see if the quadratic equation (in quadratic form) is or is not factorable. Solve for the variable and then solve for x.

v=x%5E2
v%5E2-35v%2B304=0----this might be all you need as your answer, OR

...
discrim=35%5E2-4%2A304=9, so you should be able to FACTOR the quadratic expression.
Look at 304.
304=2%2A152=2%2A2%2A76=2%2A2%2A2%2A2%2A38=2%2A2%2A2%2A2%2A2%2A19, but another way is to look for all of the two-factor factorizations of 304.
More comfortable might be just use the general solution to find v...

v=%2835%2B-+sqrt%289%29%29%2F2
v=%2835%2B-+3%29%2F2
highlight%28v=16%29 or highlight%28v=19%29.

Now find x.
x%5E2=16
highlight%28x=-4%29 or highlight%28x=4%29
OR
highlight%28x=-sqrt%2819%29%29 or highlight%28x=sqrt%2819%29%29


Like just said, if you do not yet know about the general solution you CAN factor the quadratic expression; it just requires looking for the right two factors for 304.