Question

Factor the expression over the complex numbers. x2+36 Enter your answer in the box.

the x2 is squared

Answer 1

hope this help Answer:( x - 3i√2)(x + 3i√2)

solve x² + 18 = 0

x² = - 18 ⇒ x = ±√- 18 = ±3i√2

factors are ( x - (3i√2))(x - (-3i√2))

x² + 18 = (x - 3i√2)(x + 3i√2

Explanation:

Answer 2

`x^(2)+36=(x-6i)(x+6i)`

Explanation:

The given expression is

`x^(2)+36`

It's understood that this expression is equal to zero

`x^(2) +36=0`

Now, we isolate the variable and then apply a squared root to each side of the equation

`x^(2)=-36\\x=\±√(-36)`

At this point, you'll find that the equation doesn't have solution in the real numbers, that is, all solutions are in the complex numbers. We need to add the imaginary number
`i=√(-1)` to continue

`x=\±√(-36)\\x=\±√(36)i\\x=\±6i\\\\x_(1)=6i\\x_(2)=-6i`

Now, representing these solution as factors, we would have

`x-6i=0\\x+6i=0`

Finally,

`x^(2)+36=(x-6i)(x+6i)`