Finite Math Examples

$x (460 - 2 x)$

Step 1

Set $x (460 - 2 x)$ equal to $0$ .

$x (460 - 2 x) = 0$

Step 2

Simplify the left side.

Tap for more steps...

Step 2.1

Simplify $x (460 - 2 x)$ .

Tap for more steps...

Step 2.1.1

Simplify by multiplying through.

Tap for more steps...

Step 2.1.1.1

Apply the distributive property.

$x \cdot 460 + x (- 2 x) = 0$

Step 2.1.1.2

Reorder.

Tap for more steps...

Step 2.1.1.2.1

Move $460$ to the left of $x$ .

$460 \cdot x + x (- 2 x) = 0$

Step 2.1.1.2.2

Rewrite using the commutative property of multiplication.

$460 \cdot x - 2 x \cdot x = 0$

Step 2.1.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 2.1.2.1

Move $x$ .

$460 x - 2 (x \cdot x) = 0$

Step 2.1.2.2

Multiply $x$ by $x$ .

$460 x - 2 x^{2} = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = - 2$ , $b = 460$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{- 460 \pm \sqrt{460^{2} - 4 \cdot (- 2 \cdot 0)}}{2 \cdot - 2}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the numerator.

Tap for more steps...

Step 5.1.1

Raise $460$ to the power of $2$ .

$x = \frac{- 460 \pm \sqrt{211600 - 4 \cdot - 2 \cdot 0}}{2 \cdot - 2}$

Step 5.1.2

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

Tap for more steps...

Step 5.1.2.1

Multiply $- 4$ by $- 2$ .

$x = \frac{- 460 \pm \sqrt{211600 + 8 \cdot 0}}{2 \cdot - 2}$

Step 5.1.2.2

Multiply $8$ by $0$ .

$x = \frac{- 460 \pm \sqrt{211600 + 0}}{2 \cdot - 2}$

Step 5.1.3

Add $211600$ and $0$ .

$x = \frac{- 460 \pm \sqrt{211600}}{2 \cdot - 2}$

Step 5.1.4

Rewrite $211600$ as $460^{2}$ .

$x = \frac{- 460 \pm \sqrt{460^{2}}}{2 \cdot - 2}$

Step 5.1.5

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

$x = \frac{- 460 \pm 460}{2 \cdot - 2}$

Step 5.2

Multiply $2$ by $- 2$ .

$x = \frac{- 460 \pm 460}{- 4}$

Step 5.3

Simplify $\frac{- 460 \pm 460}{- 4}$ .

$x = 115 \pm 115$

Step 6

The final answer is the combination of both solutions.

$x = 230, 0$