SOLUTION: Solve. {{{w^4-18w^2-2=0}}}

Question 390276: Solve.

Found 2 solutions by nerdybill, richard1234:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!

.
Let x =
now, we can rewrite our equation as:
.

applying the quadratic formula, we get:
x = {18.1104, -0.1104}
.
since w^2 = x
w =
x = {4.256}
.
details of quadratic follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=332 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 18.1104335791443, -0.110433579144299. Here's your graph:

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Letting , substitute:

By the quadratic formula, If then . Likewise, if then (this gives two real and two complex values for w).
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