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

Question

1610 views around the world

You can reuse this answer
Creative Commons License

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.