Algebra Examples

$x^{2} - 81 = 0$

Step 1

Rewrite $81$ as $9^{2}$ .

$x^{2} - 9^{2} = 0$

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 $b = 9$ .

$(x + 9) (x - 9) = 0$

Step 3

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

$x + 9 = 0$

$x - 9 = 0$

Step 4

Set $x + 9$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Step 4.2

Subtract $9$ from both sides of the equation.

$x = - 9$

Step 5

Set $x - 9$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Step 5.2

Add $9$ to both sides of the equation.

$x = 9$

Step 6

The final solution is all the values that make $(x + 9) (x - 9) = 0$ true.

$x = - 9, 9$