Question

Solve by factoring or finding square roots. x^2+2x+1=0

Answer 1

x = -1

Explanation:

We have given a quadratic equation.

x²+2x+1 = 0

We have to solve above equation by factoring.

Split the middle term of above equation so that the sum of two terms should be 2 and the product is 1, we have

x²+x+x+1 = 0

Making two groups and taking common, we have

x(x+1)+1(x+1) = 0

Taking (x+1) as common, we have

(x+1)(x+1) = 0

Applying Zero-Product Property to above equation, we have

x+1= 0 or x+1 = 0

x= -1 or x = -1

Both values are same.

Hence,

x = -1 is solution of given equation.

Answer 2

x=-1

Explanation:

x^2+2x+1=0

What 2 numbers multiply to 1 and add to 2

1*1 = 1

1+1=2

(x+1) (x+1) =0

Using the zero product property

x+1 = 0 x+1 = 0

x=-1 x=-1

x=-1