Solve Using the Quadratic Formula k^2-3k-10=0

$k^{2} - 3 k - 10 = 0$

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 $a = 1$ , $b = - 3$ , and $c = - 10$ into the quadratic formula and solve for $k$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (1 \cdot - 10)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 3$ to the power of $2$ .

$k = \frac{3 \pm \sqrt{9 - 4 \cdot 1 \cdot - 10}}{2 \cdot 1}$

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

Multiply $- 4$ by $1$ .

$k = \frac{3 \pm \sqrt{9 - 4 \cdot - 10}}{2 \cdot 1}$

Multiply $- 4$ by $- 10$ .

$k = \frac{3 \pm \sqrt{9 + 40}}{2 \cdot 1}$

Add $9$ and $40$ .

$k = \frac{3 \pm \sqrt{49}}{2 \cdot 1}$

Rewrite $49$ as $7^{2}$ .

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

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

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

Multiply $2$ by $1$ .

$k = \frac{3 \pm 7}{2}$

Step 4

The final answer is the combination of both solutions.

$k = 5, - 2$