Question

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

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

Step-by-step explanation:

Answer 2

Answer:

$x^{2}+36=(x-6i)(x+6i)$

Step-by-step 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

$x^{2}=-36\\x=\±\sqrt{-36}$

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 $i=\sqrt{-1}$ to continue

$x=\±\sqrt{-36}\\x=\±\sqrt{36}i\\x=\±6i\\\\x_{1}=6i\\x_{2}=-6i$

Now, representing these solution as factors, we would have

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

Finally,

$x^{2}+36=(x-6i)(x+6i)$