SOLUTION: how you do this problem 5^3+30x^2+45x=0

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Question 216560: how you do this problem
5^3+30x^2+45x=0
Found 2 solutions by Earlsdon, drj:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
5x%5E3%2B30x%5E2%2B45x+=+0 First, factor the common factor of 5x
5x%28x2%2B6x%2B9%29+=+0 so...
5x+=+0 or x%5E2%2B6x%2B9+=+0
If 5x+=+0 then x+=+0 and...
x%5E2%2B6x%2B9+=+0 Factor the trinomial.
%28x%2B3%29%28x%2B3%29+=+0 so...
x%2B3+=+0 or x%2B3+=+0 which means that:
x+=+-3 or x+=+-3 This is a "double" root.
The answer is:
x+=+0
x+=+-3
x+=+-3
graph%28400%2C400%2C-5%2C3%2C-5%2C5%2C5x%5E3%2B30x%5E2%2B45x%29

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
How you do this problem

5%5E3%2B30x%5E2%2B45x=0

Step 1. Rewrite the equation in descending order

30x%5E2%2B45x%2B5%5E2=0

30x%5E2%2B45x%2B125 where 5^3=5*5*5=125.

Step 2. Let's factor out the 5

5%2A%286x%5E2%2B9x%2B25%29=0

Step 2. Use the quadratic formula to solve this quadratic equation given as

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

where a=6, b=9, and c=25

Please ignore the graph below since we are dealing with imaginary numbers as shown in the solution below.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B9x%2B25+=+0) has the following solutons:

x%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=%289%29%5E2-4%2A6%2A25=-519.

The discriminant -519 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -519 is + or - sqrt%28+519%29+=+22.781571499789.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B9%2Ax%2B25+%29



I hope the above steps 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.

Good luck in your studies!

Respectfully,
Dr J