Solve Using the Quadratic Formula 2x^2+7x+5=0

$2 x^{2} + 7 x + 5 = 0$

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 $a = 2$ , $b = 7$ , and $c = 5$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (2 \cdot 5)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 2 \cdot 5}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 5$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 8 \cdot 5}}{2 \cdot 2}$

Multiply $- 8$ by $5$ .

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

Subtract $40$ from $49$ .

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

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

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

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

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

Multiply $2$ by $2$ .

$x = \frac{- 7 \pm 3}{4}$

Step 4

The final answer is the combination of both solutions.

$x = - 1, - \frac{5}{2}$