How do you simplify (x^2+9)?

Question

I simplified it down to that and i know you can still simplify more cause its a squared root but what would be the answer? PLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLlZZZZZZZZZZZZZZZZZZZ Help!

Answer 1

I'm assuming all the signs are correct. 

You cannot simplify x^2 + 9 with real numbers but you can use the imaginary number system.

i =√(-1)   or i^2=-1

 

x^2 + 9

simplifies to 

(x - 3i)(x + 3i)

 

So the whole expression would read

(x+3)(x-3i)(x+3i)=0

 

or 

 

But if you are looking to evaluate the entire expression...

One solution is x=-3 because

you should have (x+3)(x^2+9)=0  and if x=-3 then you have (0)(a quantity) or the zero product property. 

 

3 solutions for x: -3, 3i and -3i 

 

 

 

 

 

 

Answer 2

x³ + 3x² + 9x + 27 = 0

 

(x + 3)(x² + 9) = 0

 

This is as far as this can be factored Ashleigh.  Do they want you to find the zeros?  If so, there is only one: x = -3.

Answer 3

Hi Ashleigh;

(x³+3x²) + (9x+27)= 0

Let's remove the parentheses...

x³+3x²+9x+27= 0

For the FOIL...

FIRST must be (x²)(x).

OUTER must be (x²)(3).

INNER must be (9)(x).

LAST must be (9)(3).

(x²+9)(x+3)=0

Let's FOIL...

FIRST...(x²)(x)=x³

OUTER...(x²)(3)=3x²

INNER...(9)(x)=9x

LAST...(9)(3)=27

x³+3x²+9x+27=0

(x²+9)(x+3)=0

Either or both parenthetical equation(s) must equal zero.

x²+9=0

x²=-9

no result.  x² will always have a positive result.

x+3=0

x=-3