Solve Using the Quadratic Formula b^2+11b+30=0

$b^{2} + 11 b + 30 = 0$

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 $a = 1$ , $b = 11$ , and $c = 30$ into the quadratic formula and solve for $b$ .

$\frac{- 11 \pm \sqrt{11^{2} - 4 \cdot (1 \cdot 30)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $11$ to the power of $2$ .

$b = \frac{- 11 \pm \sqrt{121 - 4 \cdot 1 \cdot 30}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 30$ .

Multiply $- 4$ by $1$ .

$b = \frac{- 11 \pm \sqrt{121 - 4 \cdot 30}}{2 \cdot 1}$

Multiply $- 4$ by $30$ .

$b = \frac{- 11 \pm \sqrt{121 - 120}}{2 \cdot 1}$

Subtract $120$ from $121$ .

$b = \frac{- 11 \pm \sqrt{1}}{2 \cdot 1}$

Any root of $1$ is $1$ .

$b = \frac{- 11 \pm 1}{2 \cdot 1}$

Multiply $2$ by $1$ .

$b = \frac{- 11 \pm 1}{2}$

Step 4

The final answer is the combination of both solutions.

$b = - 5, - 6$