Answer:
[tex](x+5\sqrt{2}i)(x-5\sqrt{2}i)[/tex]
Step-by-step explanation:
The factorization is in the form (x-a)(x-b) where a,b are zeros of the equation [tex]x^{2} +50=0[/tex].
[tex]x^{2} =-50[/tex]
[tex]x =\sqrt{-50}[/tex]
[tex]x =\sqrt{50}i = 5\sqrt{2}i[/tex] and [tex]x =-\sqrt{50}i = -5\sqrt{2}i[/tex]
So, the factorization is [tex](x+5\sqrt{2}i)(x-5\sqrt{2}i)[/tex]
Complex numbers are numbers with real and imaginary part.
The factorized expression is [tex]\mathbf{x^2 + 50 = (x^2 +5i\sqrt 2)(x^2 -5i\sqrt 2) }[/tex]
The expression is given as:
[tex]\mathbf{x^2 + 50}[/tex]
Set to 0
[tex]\mathbf{x^2 + 50 = 0}[/tex]
Subtract 50 from both sides
[tex]\mathbf{x^2 = -50}[/tex]
Take square roots
[tex]\mathbf{x = \sqrt{-50}}[/tex]
Expand
[tex]\mathbf{x = \sqrt{25 \times -2}}[/tex]
Take square roots of 25
[tex]\mathbf{x =\pm 5\sqrt{-2}}[/tex]
Expand
[tex]\mathbf{x = \pm5\sqrt{2 \times -1}}[/tex]
Split
[tex]\mathbf{x =\pm 5\sqrt{2} \times \sqrt{-1}}[/tex]
In complex numbers,
[tex]\mathbf{\sqrt{-1} = i}[/tex]
So, we have:
[tex]\mathbf{x = \pm5i\sqrt{2}}[/tex]
So, we have:
[tex]\mathbf{x^2 + 50 = (x^2 +5i\sqrt 2)(x^2 -5i\sqrt 2) }[/tex]
Read more about complex numbers at:
https://brainly.com/question/11227018
