Question

Solve the equation
`x^2+25=0` by factoring.

Answer 1

x = 5i

x = -5i

Explanation:

x² + 25 = 0

x² = 0 - 25

x² = -25

x = √-25

x = 5i

Answer 2

x = 5i x =-5i

Explanation:

x^2+25=0

Rewriting

x^2 - (-25)=0

Writing as the difference of squares

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

where a = x and b = (sqrt(-25)) =±5i

( x-5i) ( x+5i) =0

Using the zero product property

x-5i =0 x+5i =0

x = 5i x =-5i