Solve Using the Quadratic Formula 25x^2+300x=0

$25 x^{2} + 300 x = 0$

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 $a = 25$ , $b = 300$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{- 300 \pm \sqrt{300^{2} - 4 \cdot (25 \cdot 0)}}{2 \cdot 25}$

Step 3

Simplify.

Simplify the numerator.

Raise $300$ to the power of $2$ .

$x = \frac{- 300 \pm \sqrt{90000 - 4 \cdot 25 \cdot 0}}{2 \cdot 25}$

Multiply $- 4 \cdot 25 \cdot 0$ .

Multiply $- 4$ by $25$ .

$x = \frac{- 300 \pm \sqrt{90000 - 100 \cdot 0}}{2 \cdot 25}$

Multiply $- 100$ by $0$ .

$x = \frac{- 300 \pm \sqrt{90000 + 0}}{2 \cdot 25}$

Add $90000$ and $0$ .

$x = \frac{- 300 \pm \sqrt{90000}}{2 \cdot 25}$

Rewrite $90000$ as $300^{2}$ .

$x = \frac{- 300 \pm \sqrt{300^{2}}}{2 \cdot 25}$

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

$x = \frac{- 300 \pm 300}{2 \cdot 25}$

Multiply $2$ by $25$ .

$x = \frac{- 300 \pm 300}{50}$

Simplify $\frac{- 300 \pm 300}{50}$ .

$x = - 6 \pm 6$

Step 4

The final answer is the combination of both solutions.

$x = 0, - 12$