Pre-Algebra Examples

$x \cdot x = x$

Step 1

Simplify $x \cdot x$ .

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Step 1.1

Rewrite.

$0 + 0 + x \cdot x = x$

Step 1.2

Simplify by adding zeros.

$x \cdot x = x$

Step 1.3

Multiply $x$ by $x$ .

$x^{2} = x$

Step 2

Subtract $x$ from both sides of the equation.

$x^{2} - x = 0$

Step 3

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

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Step 3.1

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

$x \cdot x - x = 0$

Step 3.2

Factor $x$ out of $- x$ .

$x \cdot x + x \cdot - 1 = 0$

Step 3.3

Factor $x$ out of $x \cdot x + x \cdot - 1$ .

$x (x - 1) = 0$

Step 4

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

$x = 0$

$x - 1 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $x - 1$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 6.2

Add $1$ to both sides of the equation.

$x = 1$

Step 7

The final solution is all the values that make $x (x - 1) = 0$ true.

$x = 0, 1$