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

1 Answer
Alan P. ยท 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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