SOLUTION: find all real solutions of the equations : (x^2 +1)^2 - 18( x^2 +1) = -17

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Question 462550: find all real solutions of the equations : (x^2 +1)^2 - 18( x^2 +1) = -17
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!



...you can solve it as quadratic using quadratic formula, you will just have four solutions; both solutions as quadratic equation you will take positive i negative value of their square root
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic





the general solution using the quadratic equation is:







So lets solve ( notice , , and )





Plug in a=1, b=-16, and c=17




Negate -16 to get 16




Square -16 to get 256 (note: remember when you square -16, 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 1 to get 2


So now the expression breaks down into two parts


or



Now break up the fraction



or



Simplify



or



So the solutions are:

or




So yoursolutions are:
or

or
or
or
so, your solutions are:






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