How do you solve #x^2-4=-3x^2-24#?

1 Answer
Alan P. · George C.
Oct 3, 2016

There are no Real solutions (as demonstrated below).
If Complex solutions are permitted #x=isqrt(5) or -isqrt(5)#

Explanation:

Given
#color(white)("XXX")x^2-4=-3x^2-24#

Get all terms with the variable #x# on the left side
by adding #3x^2# to both sides:
#color(white)("XXX")4x^2-4=-24#

Get all the constant terms on the right side
by adding #4# to both sides:
#color(white)("XXX")4x^2=-20#

Divide both sides by #4#
#color(white)("XXX")x^2=-5#

Take the square root of both sides
#color(white)("XXX")x=+-sqrt(-5)#

...as noted in the answer there are no Real solutions;
but among Complex numbers #sqrt(-1)=i# and #sqrt(-5)=isqrt(5)#

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