How do you solve x^2-75=0?

1 Answer
Alan P.
Aug 17, 2016

x=+-5sqrt(3)

Explanation:

Treat x^2-75 as the difference of squares

We know that a^2-b^2=(a-b)(a+b)

So replacing a with x
and b with 5sqrt(3) (so that b^2=75)
we have
color(white)("XXX")x^2-75=0
is equivalent to
color(white)("XXX")(x-5sqrt(3))(x+5sqrt(3))=0

which implies
either (x-5sqrt(3))=0 color(white)("XX")orcolor(white)("XX") (x+5sqrt(3))=0
color(white)("XX")rarr x=5sqrt(3)color(white)("XXXXXXXX")rarrx=-5sqrt(3)

Related questions
See all questions in Use Square Roots to Solve Quadratic Equations
Impact of this question
4816 views around the world
You can reuse this answer
Creative Commons License