Solve Using the Quadratic Formula -12x^2+600x=0

$- 12 x^{2} + 600 x = 0$

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 $a = - 12$ , $b = 600$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{- 600 \pm \sqrt{600^{2} - 4 \cdot (- 12 \cdot 0)}}{2 \cdot - 12}$

Step 3

Simplify.

Simplify the numerator.

Raise $600$ to the power of $2$ .

$x = \frac{- 600 \pm \sqrt{360000 - 4 \cdot - 12 \cdot 0}}{2 \cdot - 12}$

Multiply $- 4 \cdot - 12 \cdot 0$ .

Multiply $- 4$ by $- 12$ .

$x = \frac{- 600 \pm \sqrt{360000 + 48 \cdot 0}}{2 \cdot - 12}$

Multiply $48$ by $0$ .

$x = \frac{- 600 \pm \sqrt{360000 + 0}}{2 \cdot - 12}$

Add $360000$ and $0$ .

$x = \frac{- 600 \pm \sqrt{360000}}{2 \cdot - 12}$

Rewrite $360000$ as $600^{2}$ .

$x = \frac{- 600 \pm \sqrt{600^{2}}}{2 \cdot - 12}$

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

$x = \frac{- 600 \pm 600}{2 \cdot - 12}$

Multiply $2$ by $- 12$ .

$x = \frac{- 600 \pm 600}{- 24}$

Simplify $\frac{- 600 \pm 600}{- 24}$ .

$x = 25 \pm 25$

Step 4

The final answer is the combination of both solutions.

$x = 50, 0$