How to factor the equation x^2+13=0.

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We have to factor the equation x^2 + 13 = 0

Now we can write x^2 + 13 = 0 in the form (x - a)(x - b) =0

where a and b would be the roots of the equation.

For x^2 + 13 = 0

x^2 = -13

=> x = -i*sqrt 13 and +i*sqrt 13

a = -i*sqrt 13 and b = +i*sqrt 13

So (x - a)(x - b) =0

=> ( x + i*sqrt 13)(x - i*sqrt 13) = 0

The required result is x^2 + 13 = ( x + i*sqrt 13)(x - i*sqrt 13) = 0

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x^2 + 13 = 0

We will factor using the difference between the squares.

We know that:

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

let us rewrite:

x^2 - (-13) = 0

Now we will factor:

==> (x^2-(-13) = 0

==> (x-sqrt-13) ( x+sqrt-13) = 0

But we know that sqrt-13 = sqrt13*i

==> (x-sqrt13*i)(x+sqrt13*i) = 0

==> x^2 +13 = (x-sqrt13*i)(x+sqrt13*i)  = 0

==> x1= sqrt13*i

==> x2= -sqrt13*i

Approved by eNotes Editorial Team

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