Solve Using the Quadratic Formula y^2+17y+72=0

$y^{2} + 17 y + 72 = 0$

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 $a = 1$ , $b = 17$ , and $c = 72$ into the quadratic formula and solve for $y$ .

$\frac{- 17 \pm \sqrt{17^{2} - 4 \cdot (1 \cdot 72)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $17$ to the power of $2$ .

$y = \frac{- 17 \pm \sqrt{289 - 4 \cdot 1 \cdot 72}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 72$ .

Multiply $- 4$ by $1$ .

$y = \frac{- 17 \pm \sqrt{289 - 4 \cdot 72}}{2 \cdot 1}$

Multiply $- 4$ by $72$ .

$y = \frac{- 17 \pm \sqrt{289 - 288}}{2 \cdot 1}$

Subtract $288$ from $289$ .

$y = \frac{- 17 \pm \sqrt{1}}{2 \cdot 1}$

Any root of $1$ is $1$ .

$y = \frac{- 17 \pm 1}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{- 17 \pm 1}{2}$

Step 4

The final answer is the combination of both solutions.

$y = - 8, - 9$