Finite Math Examples

$\frac{1}{2} x^{2} - 2 x = 0$

Step 1

Combine $\frac{1}{2}$ and $x^{2}$ .

$\frac{x^{2}}{2} - 2 x = 0$

Step 2

Multiply each term in $\frac{x^{2}}{2} - 2 x = 0$ by $2$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{x^{2}}{2} - 2 x = 0$ by $2$ .

$\frac{x^{2}}{2} \cdot 2 - 2 x \cdot 2 = 0 \cdot 2$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{x^{2}}{2} \cdot 2 - 2 x \cdot 2 = 0 \cdot 2$

Step 2.2.1.1.2

Rewrite the expression.

$x^{2} - 2 x \cdot 2 = 0 \cdot 2$

Step 2.2.1.2

Multiply $2$ by $- 2$ .

$x^{2} - 4 x = 0 \cdot 2$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $0$ by $2$ .

$x^{2} - 4 x = 0$

Step 3

Factor $x$ out of $x^{2} - 4 x$ .

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Step 3.1

Factor $x$ out of $x^{2}$ .

$x \cdot x - 4 x = 0$

Step 3.2

Factor $x$ out of $- 4 x$ .

$x \cdot x + x \cdot - 4 = 0$

Step 3.3

Factor $x$ out of $x \cdot x + x \cdot - 4$ .

$x (x - 4) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 4 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $x - 4$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 6.2

Add $4$ to both sides of the equation.

$x = 4$

Step 7

The final solution is all the values that make $x (x - 4) = 0$ true.

$x = 0, 4$