Algebra Examples

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

Step 1

Eliminate the equal sides of each equation and combine.

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

Step 2

Solve $x - 2 = x^{2} - 2$ for $x$ .

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Step 2.1

Subtract $x^{2}$ from both sides of the equation.

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

Step 2.2

Add $2$ to both sides of the equation.

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

Step 2.3

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

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Step 2.3.1

Add $- 2$ and $2$ .

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

Step 2.3.2

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

$x - x^{2} = 0$

Step 2.4

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

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Step 2.4.1

Factor $x$ out of $x^{1}$ .

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

Step 2.4.2

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

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

Step 2.4.3

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

$x (1 - x) = 0$

Step 2.5

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

$x = 0$

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

Step 2.6

Set $x$ equal to $0$ .

$x = 0$

Step 2.7

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

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Step 2.7.1

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

$1 - x = 0$

Step 2.7.2

Solve $1 - x = 0$ for $x$ .

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Step 2.7.2.1

Subtract $1$ from both sides of the equation.

$- x = - 1$

Step 2.7.2.2

Divide each term in $- x = - 1$ by $- 1$ and simplify.

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Step 2.7.2.2.1

Divide each term in $- x = - 1$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 1}{- 1}$

Step 2.7.2.2.2

Simplify the left side.

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Step 2.7.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 1}{- 1}$

Step 2.7.2.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 1}{- 1}$

Step 2.7.2.2.3

Simplify the right side.

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Step 2.7.2.2.3.1

Divide $- 1$ by $- 1$ .

$x = 1$

Step 2.8

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

$x = 0, 1$

Step 3

Evaluate $y$ when $x = 0$ .

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Step 3.1

Substitute $0$ for $x$ .

$y = {(0)}^{2} - 2$

Step 3.2

Substitute $0$ for $x$ in $y = {(0)}^{2} - 2$ and solve for $y$ .

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Step 3.2.1

Remove parentheses.

$y = 0^{2} - 2$

Step 3.2.2

Simplify $0^{2} - 2$ .

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Step 3.2.2.1

Raising $0$ to any positive power yields $0$ .

$y = 0 - 2$

Step 3.2.2.2

Subtract $2$ from $0$ .

$y = - 2$

Step 4

Evaluate $y$ when $x = 1$ .

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Step 4.1

Substitute $1$ for $x$ .

$y = {(1)}^{2} - 2$

Step 4.2

Substitute $1$ for $x$ in $y = {(1)}^{2} - 2$ and solve for $y$ .

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Step 4.2.1

Remove parentheses.

$y = 1^{2} - 2$

Step 4.2.2

Simplify $1^{2} - 2$ .

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Step 4.2.2.1

One to any power is one.

$y = 1 - 2$

Step 4.2.2.2

Subtract $2$ from $1$ .

$y = - 1$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(0, - 2)$

$(1, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, - 2), (1, - 1)$

Equation Form:

$x = 0, y = - 2$

$x = 1, y = - 1$

Step 7