Solve Using the Quadratic Formula y^2+18y+81=0

$y^{2} + 18 y + 81 = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 1$ , $b = 18$ , and $c = 81$ into the quadratic formula and solve for $y$ .

$\frac{- 18 \pm \sqrt{18^{2} - 4 \cdot (1 \cdot 81)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $18$ to the power of $2$ .

$y = \frac{- 18 \pm \sqrt{324 - 4 \cdot 1 \cdot 81}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 81$ .

Multiply $- 4$ by $1$ .

$y = \frac{- 18 \pm \sqrt{324 - 4 \cdot 81}}{2 \cdot 1}$

Multiply $- 4$ by $81$ .

$y = \frac{- 18 \pm \sqrt{324 - 324}}{2 \cdot 1}$

Subtract $324$ from $324$ .

$y = \frac{- 18 \pm \sqrt{0}}{2 \cdot 1}$

Rewrite $0$ as $0^{2}$ .

$y = \frac{- 18 \pm \sqrt{0^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$y = \frac{- 18 \pm 0}{2 \cdot 1}$

$- 18$ plus or minus $0$ is $- 18$ .

$y = \frac{- 18}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{- 18}{2}$

Divide $- 18$ by $2$ .

$y = - 9$

Step 4

The final answer is the combination of both solutions.

$y = - 9$ Double roots