Pre-Algebra Examples

$x + 2 = x^{2} - 5 x + 2$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x^{2} - 5 x + 2 = x + 2$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $x$ from both sides of the equation.

$x^{2} - 5 x + 2 - x = 2$

Step 2.2

Subtract $x$ from $- 5 x$ .

$x^{2} - 6 x + 2 = 2$

Step 3

Subtract $2$ from both sides of the equation.

$x^{2} - 6 x + 2 - 2 = 0$

Step 4

Combine the opposite terms in $x^{2} - 6 x + 2 - 2$ .

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Step 4.1

Subtract $2$ from $2$ .

$x^{2} - 6 x + 0 = 0$

Step 4.2

Add $x^{2} - 6 x$ and $0$ .

$x^{2} - 6 x = 0$

Step 5

Factor $x$ out of $x^{2} - 6 x$ .

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Step 5.1

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

$x \cdot x - 6 x = 0$

Step 5.2

Factor $x$ out of $- 6 x$ .

$x \cdot x + x \cdot - 6 = 0$

Step 5.3

Factor $x$ out of $x \cdot x + x \cdot - 6$ .

$x (x - 6) = 0$

Step 6

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

$x = 0$

$x - 6 = 0$

Step 7

Set $x$ equal to $0$ .

$x = 0$

Step 8

Set $x - 6$ equal to $0$ and solve for $x$ .

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Step 8.1

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Step 8.2

Add $6$ to both sides of the equation.

$x = 6$

Step 9

The final solution is all the values that make $x (x - 6) = 0$ true.

$x = 0, 6$