Algebra Examples

x^{2} - x = 0

$x^{2} - x = 0$

Step 1

Factor

x

$x$ out of

x^{2} - x

$x^{2} - x$ .

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Step 1.1

Factor

x

$x$ out of

x^{2}

$x^{2}$ .

x \cdot x - x = 0

$x \cdot x - x = 0$

Step 1.2

Factor

x

$x$ out of

- x

$- x$ .

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

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

Step 1.3

Factor

x

$x$ out of

x \cdot x + x \cdot - 1

$x \cdot x + x \cdot - 1$ .

x (x - 1) = 0

$x (x - 1) = 0$

x (x - 1) = 0

$x (x - 1) = 0$

Step 2

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

x = 0

$x = 0$

x - 1 = 0

$x - 1 = 0$

Step 3

Set

x

$x$ equal to

0

$0$ .

x = 0

$x = 0$

Step 4

Set

x - 1

$x - 1$ equal to

0

$0$ and solve for

x

$x$ .

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Step 4.1

Set

x - 1

$x - 1$ equal to

0

$0$ .

x - 1 = 0

$x - 1 = 0$

Step 4.2

Add

1

$1$ to both sides of the equation.

x = 1

$x = 1$

x = 1

$x = 1$

Step 5

The final solution is all the values that make

x (x - 1) = 0

$x (x - 1) = 0$ true.

x = 0, 1

$x = 0, 1$

$x^{2} - x = 0$

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