How do you solve #x^2 - 49 = 0 #?

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Answer 1 · 2016-03-17T15:59:41

#x_(1,2)=+-7#

You could use several methods.

The fastest is:

#x^2=49#

#:.sqrt(x^2)=+-sqrt(49)#

#x_(1,2)=+-7#

I'd prefer to factorize the equation using the Square Difference Identitiy:

#(a^2-b^2)=(a+b)(a-b)#

to rewrite the second degree equation as product of first degree equation.

In your exercise:

#(x^2-49)=0 <=>(x^2-7^2)=0 <=>(x+7)(x-7)=0#

A product is zero when the factors are zero

#:.(x+7)=0=>x_1=-7#
#:.(x-7)=0=>x_2=7#

Therefore:

#x_(1,2)=+-7#