Solve Using the Quadratic Formula d^2+7d+10=0

$d^{2} + 7 d + 10 = 0$

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 $a = 1$ , $b = 7$ , and $c = 10$ into the quadratic formula and solve for $d$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (1 \cdot 10)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$d = \frac{- 7 \pm \sqrt{49 - 4 \cdot 1 \cdot 10}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 10$ .

Multiply $- 4$ by $1$ .

$d = \frac{- 7 \pm \sqrt{49 - 4 \cdot 10}}{2 \cdot 1}$

Multiply $- 4$ by $10$ .

$d = \frac{- 7 \pm \sqrt{49 - 40}}{2 \cdot 1}$

Subtract $40$ from $49$ .

$d = \frac{- 7 \pm \sqrt{9}}{2 \cdot 1}$

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

$d = \frac{- 7 \pm \sqrt{3^{2}}}{2 \cdot 1}$

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

$d = \frac{- 7 \pm 3}{2 \cdot 1}$

Multiply $2$ by $1$ .

$d = \frac{- 7 \pm 3}{2}$

Step 4

The final answer is the combination of both solutions.

$d = - 2, - 5$