SOLUTION: Help me solve this polynomial equation algebraically: (12x^4) - (3x^2) - 54 = 0

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Question 717596: Help me solve this polynomial equation algebraically:
(12x^4) - (3x^2) - 54 = 0
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Divide left and right members by 3. Substitute for x^2 as a different single variable and solve for that variable; and then reverse the subsitution to continue solving for x.

Your equation is the same as 4x%5E4-x%5E2-18=0.

You could ignore the substitution for x^2 suggestion and go along with x^2 as the variable, and THEN continue on for x. The simpler equation on the left side is factorable, so you now have %284x%5E2-9%29%28x%5E2%2B2%29=0.

For x^2+2=0, no real solution. Complex solution yes. No real one. i%2Asqrt%282%29=x or -i%2Asqrt%282%29.

For 4x^2-9=0, 4x^2=9, x^2=9/4, x=%2B3%2F2 or x=-3%2F2.