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

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

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 $a = 2$ , $b = 5$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (2 \cdot 0)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $5$ to the power of $2$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 2 \cdot 0}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 0$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 5 \pm \sqrt{25 - 8 \cdot 0}}{2 \cdot 2}$

Multiply $- 8$ by $0$ .

$x = \frac{- 5 \pm \sqrt{25 + 0}}{2 \cdot 2}$

Add $25$ and $0$ .

$x = \frac{- 5 \pm \sqrt{25}}{2 \cdot 2}$

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

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

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

$x = \frac{- 5 \pm 5}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 5 \pm 5}{4}$

Step 4

The final answer is the combination of both solutions.

$x = 0, - \frac{5}{2}$