What are the solutions of 2x^2 -3=13?

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Answer 1 · 2018-05-21T17:08:18

After some minor re-arranging, we can find that the solutions are #x=+-2sqrt(2)#

First, we'll get all the constants to one side, and all of the #x#-related coefficients on the other:

#2x^2cancel(-3)color(red)(cancel(+3))=13color(red)(+3)#

#2x^2=16#

Next, we'll divide through by #x#'s coefficient:

#(cancel(2)x^2)/color(red)(cancel(2))=16/color(red)(2)#

#x^2=8#

Finally, we'll take the square root of both sides:

#sqrt(x^2)=sqrt(8)#

#x=sqrt(8)#

#x=sqrt(4xx2)#

#x=sqrt(4)xxsqrt(2)#

#color(green)(x=+-2sqrt(2))#

The reason why that counts as two solutions is because any number squared, regardless of if it is positive or negative, results in a positive number.