Solve Using the Quadratic Formula 2k^2+9k=-7

$2 k^{2} + 9 k = - 7$

Step 1

Add $7$ to both sides of the equation.

$2 k^{2} + 9 k + 7 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 2$ , $b = 9$ , and $c = 7$ into the quadratic formula and solve for $k$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (2 \cdot 7)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

Raise $9$ to the power of $2$ .

$k = \frac{- 9 \pm \sqrt{81 - 4 \cdot 2 \cdot 7}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 7$ .

Multiply $- 4$ by $2$ .

$k = \frac{- 9 \pm \sqrt{81 - 8 \cdot 7}}{2 \cdot 2}$

Multiply $- 8$ by $7$ .

$k = \frac{- 9 \pm \sqrt{81 - 56}}{2 \cdot 2}$

Subtract $56$ from $81$ .

$k = \frac{- 9 \pm \sqrt{25}}{2 \cdot 2}$

Rewrite $25$ as $5^{2}$ .

$k = \frac{- 9 \pm \sqrt{5^{2}}}{2 \cdot 2}$

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

$k = \frac{- 9 \pm 5}{2 \cdot 2}$

Multiply $2$ by $2$ .

$k = \frac{- 9 \pm 5}{4}$

Step 5

The final answer is the combination of both solutions.

$k = - 1, - \frac{7}{2}$