Find the Discriminant y^2+6y+9=0

$y^{2} + 6 y + 9 = 0$

Step 1

Solve the equation for $y$ .

Factor using the perfect square rule.

Rewrite $9$ as $3^{2}$ .

$y^{2} + 6 y + 3^{2} = 0$

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

$6 y = 2 \cdot y \cdot 3$

Rewrite the polynomial.

$y^{2} + 2 \cdot y \cdot 3 + 3^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = y$ and $b = 3$ .

${(y + 3)}^{2} = 0$

Set the $y + 3$ equal to $0$ .

$y + 3 = 0$

Subtract $3$ from both sides of the equation.

$y = - 3$

Step 2

Since $- 3 \neq 0$ , there are no solutions.

No solution