How do you solve the equation #2/3x^2-4=12#?

1 Answer
Jun 12, 2017

Answer:

The answer is #x=+-2sqrt6#.
.

Explanation:

Solve:

#2/3x^2-4=12#

Add #4# to both sides.

#2/3x^2-color(red)cancel(color(black)(4))+color(red)cancel(color(black)(4))=12+4#

Simplify.

#2/3x^2=16#

Multiply both sides by #3#.

#color(red)cancel(color(black)(3))xx2/color(red)cancel(color(black)(3))x^2=16xx3#

Simplify.

#2x^2=48#

Divide both sides by #2#.

#color(red)cancel(color(black)(2))/color(red)cancel(color(black)(2))x^2=48/2#

Simplify.

#x^2=24#

Take the square root of both sides.

#sqrt(x^2)=+-sqrt24#

Simplify.

#x=+-sqrt24#

Simplify #sqrt24# using prime factorization.

#x=+-sqrt(2xx2xx2xx3)#

#x=+-sqrt(2^2xx2xx3)#

#x=+-2sqrt6#