Solve Using the Quadratic Formula 2y^2+14y=-19

$2 y^{2} + 14 y = - 19$

Step 1

Add $19$ to both sides of the equation.

$2 y^{2} + 14 y + 19 = 0$

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 $a = 2$ , $b = 14$ , and $c = 19$ into the quadratic formula and solve for $y$ .

$\frac{- 14 \pm \sqrt{14^{2} - 4 \cdot (2 \cdot 19)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

Raise $14$ to the power of $2$ .

$y = \frac{- 14 \pm \sqrt{196 - 4 \cdot 2 \cdot 19}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 19$ .

Multiply $- 4$ by $2$ .

$y = \frac{- 14 \pm \sqrt{196 - 8 \cdot 19}}{2 \cdot 2}$

Multiply $- 8$ by $19$ .

$y = \frac{- 14 \pm \sqrt{196 - 152}}{2 \cdot 2}$

Subtract $152$ from $196$ .

$y = \frac{- 14 \pm \sqrt{44}}{2 \cdot 2}$

Rewrite $44$ as $2^{2} \cdot 11$ .

Factor $4$ out of $44$ .

$y = \frac{- 14 \pm \sqrt{4 (11)}}{2 \cdot 2}$

Rewrite $4$ as $2^{2}$ .

$y = \frac{- 14 \pm \sqrt{2^{2} \cdot 11}}{2 \cdot 2}$

Pull terms out from under the radical.

$y = \frac{- 14 \pm 2 \sqrt{11}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$y = \frac{- 14 \pm 2 \sqrt{11}}{4}$

Simplify $\frac{- 14 \pm 2 \sqrt{11}}{4}$ .

$y = \frac{- 7 \pm \sqrt{11}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{- 7 \pm \sqrt{11}}{2}$

Decimal Form:

$y = - 1.84168760 \dots, - 5.15831239 \dots$