SOLUTION: Solve. 6x^4-19x^2+10=0 I tried using the solver and the answer didn't look right to me. Can you show me how to solve so I can understand the steps.

Algebra.Com
Question 132426: Solve.
6x^4-19x^2+10=0
I tried using the solver and the answer didn't look right to me. Can you show me how to solve so I can understand the steps.

Found 2 solutions by checkley71, jim_thompson5910:
Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
6x^4-19x^2+10=0
(3x^2-2)(2x^2-5)=0 answer.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Which solver did you use?

Start with the given equation


Let

Plug in


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for u:


Starting with the general quadratic





the general solution using the quadratic equation is:







So lets solve ( notice , , and )





Plug in a=6, b=-19, and c=10




Negate -19 to get 19




Square -19 to get 361 (note: remember when you square -19, you must square the negative as well. This is because .)




Multiply to get




Combine like terms in the radicand (everything under the square root)




Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




Multiply 2 and 6 to get 12


So now the expression breaks down into two parts


or


Lets look at the first part:





Add the terms in the numerator

Divide


So one answer is






Now lets look at the second part:





Subtract the terms in the numerator

Divide


So another answer is




So our solutions are:

or





Remember, we let . So this means that


or


or Take the square root of both sides for each case


Break up the two expressions

, , or



-------------------------------------------------

Answer:


So our solutions are

, , or

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