Start with
[tex]x^2+75=0[/tex]
Subtract 75 from both sides:
[tex]x^2=-75[/tex]
Take the square root of both sides. As usual, this implies a double sign on the right hand side:
[tex]x=\pm\sqrt{-75}=\pm\sqrt{(-1)75}=\pm\sqrt{-1}\sqrt{75}=\pm\sqrt{75}i[/tex]
So, the two answers are
[tex]\sqrt{75}i,\quad -\sqrt{75}i[/tex]
Answer:
-5√3 i, 5√3 i.
Step-by-step explanation:
x^2 + 75 = 0
x^2 = -75
x = +/- √-75
= +/- √75 i
= +/- 5√3 i.
