SOLUTION: Hello, I need help in solving the following problem, I have tried but I do not understand how to solve the problem. Here the problem: Solve {{{t^4-11t^2+18}}} Tha

Question 246717: Hello,
I need help in solving the following problem, I have tried but I do not understand how to solve the problem.
Here the problem:

Solve

Thank you so much, I think that you guys are great to help people like me, I been out of school for 15 years and it hard trying to remember how to solve these type of problems.

Found 2 solutions by nerdybill, richwmiller:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
I assume they are asking you to factor it.
.

You could leave it like that or, you could factor the last term as:

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
We are going to use a little trick to solve this.
Substitute u for t^2
That gives us
u^2-11+18=0
we can solve with the factoring, quadratic formula or complete the square
factoring is the easiest
(u-2)(-9)=0
u=2
u=9
but u=x^2 so
+\- means plus or minus
+\-t=sqrt(u)
so we have four solutions
t=+\-sqrt(2)
t=+\-3
see below to use the quadratic formula

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=49 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9, 2. Here's your graph:

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