Question

How do you factor x^2-5=0

Answer 1

Do you remember the special case of factoring the difference of 2 squares ?

x² - 5 = (x + √5) (x - √5)

That will be zero if either factor is zero.

First factor:
x + √5 = 0
x = -√5

Second factor:
x - √5 = 0
x = √5
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Another way to look at it is just to sit there and LOOK at it.

x² - 5 = 0

x² = 5

This is true if  x = + or - √5 .