SOLUTION: 1. x^3+216=0 2. 5x^3+30x^2+45x=0 3. 1/x^2+8/x+15=0

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Question 213777: 1. x^3+216=0


2. 5x^3+30x^2+45x=0


3. 1/x^2+8/x+15=0
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
1. x^3+216=0

x%5E3%2B216-216=0-216 Subtracting 216 from both sides of equation

x%5E3=-216

x=-6 Answer

2. 5x^3+30x^2+45x=0

x%285x%5E2%2B30x%2B45%29=0

x%285x%2B+15%29%28x%2B3%29+=+0+

where we have x=0, 5x+15=0 and x+3=0. Solving yields

x=0, x=-3 and x=-3, or solve quadratic equation using following steps,

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B30x%2B45+=+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=%2830%29%5E2-4%2A5%2A45=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%2830%29%29%2F2%5C5.
Expression can be factored: 5x%5E2%2B30x%2B45+=+5%28x--3%29%2A%28x--3%29

Again, the answer is: -3, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B30%2Ax%2B45+%29




3. 1/x^2+8/x+15=0 Multiply by x^2 to get rid of denominator

x%5E2%281%2Fx%5E2%2B8%2Fx%2B15%29%2Ax%5E2=0

1%2B8x%2B15x%5E2=0

%285x%2B1%29%283x%2B1%29=0

where we have 5x+1=0 and 3x+1=0. Solving yields

So x=(-1/5) and x=(-1/3)

We can also use the quadratic formula as follows:

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 15x%5E2%2B8x%2B1+=+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=%288%29%5E2-4%2A15%2A1=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+4+%29%29%2F2%5C15+=+-0.2
x%5B2%5D+=+%28-%288%29-sqrt%28+4+%29%29%2F2%5C15+=+-0.333333333333333

Quadratic expression 15x%5E2%2B8x%2B1 can be factored:
15x%5E2%2B8x%2B1+=+15%28x--0.2%29%2A%28x--0.333333333333333%29
Again, the answer is: -0.2, -0.333333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B8%2Ax%2B1+%29



I hope the above steps were helpful.

And good luck in your studies!

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Respectfully,
Dr J