Precalculus Examples

$x^{2} - 1 = 0$

Step 1

Rewrite

$1$ as

$1^{2}$ .

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

Step 2

Since both terms are perfect squares, factor using the difference of squares formula,

$a^{2} - b^{2} = (a + b) (a - b)$ where

$a = x$ and

$b = 1$ .

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

Step 3

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

$0$ , the entire expression will be equal to

$0$ .

$x + 1 = 0$

$x - 1 = 0$

Step 4

Set

$x + 1$ equal to

$0$ and solve for

$x$ .

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Step 4.1

Set

$x + 1$ equal to

$0$ .

$x + 1 = 0$

Step 4.2

Subtract

$1$ from both sides of the equation.

$x = - 1$

Step 5

Set

$x - 1$ equal to

$0$ and solve for

$x$ .

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Step 5.1

Set

$x - 1$ equal to

$0$ .

$x - 1 = 0$

Step 5.2

Add

$1$ to both sides of the equation.

$x = 1$

Step 6

The final solution is all the values that make

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

$x = - 1, 1$

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