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What are the solutions to the equation(5x-15)^{2}= -100? Show your work.
a.) x=3+2i sqrt root 5 and x=3- 2i sqrt root 5
b.) x=3+2i and x=3- 2i
c.) x- (-i) sqrt root 5 and x= i sqrt root 5
d.) x=1 and x=5

Respuesta :

Answer:

it is c hope it helps

Step-by-step explanation:

msm555

b.) x=3+2i and x=3- 2i

Answer:

Solution given:

[tex](5x-15)²=-100[/tex]

doing square root on both side

[tex]\sqrt{(5x-15)²}=\sqrt{-100}[/tex]

5x-15=[tex]\sqrt{(-1*10²}[/tex]

since we know that i²=-1,replacing it we get

[tex]5x-15=\sqrt{i²*10²}[/tex]

5x-15=±10i

dividing both side by 5 we get

[tex]\frac{5(x-3)}{5}=\frac{±10i}{5}[/tex]

x-3=±2i

either

x=2i+3

or

x=-2i+3

x=3-2i

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