How do I solve for roots?

Question

My math packet says Solving for Roots:

I have no idea what that is.

Some example problems are

3x²-5=13

2x²+8=58

4x²-10x²+7=17

Thank you for the help

Answer 1

 

roots are the values for the variable x that make the equation true

 

3x^2-5=13

3x^2=13+5

3x^2=18

x^2=6

x=±√6

 

2x^2+8=58

2x^2=58-8

2x^2=50

x^2=25

x^2-25=0

(x-5)(x+5)=0

x-5=0

x=5

x+5=0

x=-5

 

4x^2-10x^2+7=17

-6x^2+7=17

-6x^2=17-7

-6x^2=10

x^2=-10/6

x^2=-5/3

x=±√(-5/3)

x=±√(5/3)i where i=√-1 and i is not inside the radical sign