Solve for f f^2+2f+1=0

$f^{2} + 2 f + 1 = 0$

Step 1

Factor using the perfect square rule.

Rewrite $1$ as $1^{2}$ .

$f^{2} + 2 f + 1^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 f = 2 \cdot f \cdot 1$

Rewrite the polynomial.

$f^{2} + 2 \cdot f \cdot 1 + 1^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = f$ and $b = 1$ .

${(f + 1)}^{2} = 0$

Step 2

Set the $f + 1$ equal to $0$ .

$f + 1 = 0$

Step 3

Subtract $1$ from both sides of the equation.

$f = - 1$