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

Click here to see ALL problems on Quadratic Equations

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:

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