SOLUTION: solve x^4 + 6x^2 - 27 = 0

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Question 225967: solve x^4 + 6x^2 - 27 = 0
Found 2 solutions by edjones, drj:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x^4 + 6x^2 - 27 = 0
(x^2+9)(x^2-3)=0
.
x^2=-9
x=+-3sqrt(-1)
x=+-3i
.
x^2=3
x=+-sqrt(3)
.
Ed

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4+%2B+6x%5E2+-+27+=+0

Step 1. Let y=x%5E2, then x%5E4=y%5E2.

Step 2. Then,

y%5E2%2B6y-27=0

Step 3. To solve equation in Step 2, use the quadratic formula

y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1, b=6, and c=-27

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 1y%5E2%2B6y%2B-27+=+0) has the following solutons:

y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%286%29%5E2-4%2A1%2A-27=144.

Discriminant d=144 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+144+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%286%29%2Bsqrt%28+144+%29%29%2F2%5C1+=+3
y%5B2%5D+=+%28-%286%29-sqrt%28+144+%29%29%2F2%5C1+=+-9

Quadratic expression 1y%5E2%2B6y%2B-27 can be factored:
1y%5E2%2B6y%2B-27+=+1%28y-3%29%2A%28y--9%29
Again, the answer is: 3, -9. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-27+%29



With y=3 and y=-9 or x%5E2=3 and x%5E2=-9

So x=sqrt%283%29, x=-sqrt%283%29, x=sqrt%28-9%29=3i and x=-3i where i=sqrt%28-1%29

Step 4. ANSWER: So x=sqrt%283%29, x=-sqrt%283%29, x=3i and x=-3i

I hope the above steps and explanation were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV