Linear Algebra Examples

$2 x (x - 2) + 1 = 1 - 2 x$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 2 + 1 = 1 - 2 x$

Step 1.2

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

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Step 1.2.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 2 + 1 = 1 - 2 x$

Step 1.2.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 2 + 1 = 1 - 2 x$

Step 1.3

Multiply $- 2$ by $2$ .

$2 x^{2} - 4 x + 1 = 1 - 2 x$

Step 2

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

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Step 2.1

Add $2 x$ to both sides of the equation.

$2 x^{2} - 4 x + 1 + 2 x = 1$

Step 2.2

Add $- 4 x$ and $2 x$ .

$2 x^{2} - 2 x + 1 = 1$

Step 3

Subtract $1$ from both sides of the equation.

$2 x^{2} - 2 x + 1 - 1 = 0$

Step 4

Combine the opposite terms in $2 x^{2} - 2 x + 1 - 1$ .

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Step 4.1

Subtract $1$ from $1$ .

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

Step 4.2

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

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

Step 5

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

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Step 5.1

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

$2 x (x) - 2 x = 0$

Step 5.2

Factor $2 x$ out of $- 2 x$ .

$2 x (x) + 2 x (- 1) = 0$

Step 5.3

Factor $2 x$ out of $2 x (x) + 2 x (- 1)$ .

$2 x (x - 1) = 0$

Step 6

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

$x = 0$

$x - 1 = 0$

Step 7

Set $x$ equal to $0$ .

$x = 0$

Step 8

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

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Step 8.1

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

$x - 1 = 0$

Step 8.2

Add $1$ to both sides of the equation.

$x = 1$

Step 9

The final solution is all the values that make $2 x (x - 1) = 0$ true.

$x = 0, 1$

Step 10

The domain is the set of all valid $x$ values.

${x | x = 0, 1}$

Step 11