Quadratic equations by factoring

Question

how to solve the following quadratic equation by factoring

x^2 + 9 = 0

Answer 1

This is prime, meaning it can't be factored using real numbers.

Answer 2

This is a sum of squares.  If you factor it, you will get complex numbers.

 

x² + 9 = (x - 3i)(x + 3i)

 

i = √(-1)

Answer 3

Okay, I'm going to say off the bat that if you're looking for standard numbers, then you're out of luck. the smallest x can be on the parabola  is 0, and:

0 + 9 = 9, which means the smallest possible answer is still greater than 0.

If we isolate x for example:

x² = -9

x = √-9

 

We cannot take the square root of a negative. To solve this, we need to "factor out" the -1, after a fashion:

x = √9 * √-1

x = 3 √-1

x = 3i

i is called an imaginary number, because the square root of -1 does not actually exist, but it can be a useful tool when discussing problems such as these.