Algebra Examples

$x^{2} = 9$

Subtract $9$ from both sides of the equation.

$x^{2} - 9 = 0$

Rewrite $9$ as $3^{2}$ .

$x^{2} - 3^{2} = 0$

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 $b = 3$ .

$(x + 3) (x - 3) = 0$

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

$x + 3 = 0$

$x - 3 = 0$

Set $x + 3$ equal to $0$ and solve for $x$ .

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Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Set $x - 3$ equal to $0$ and solve for $x$ .

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Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

The final solution is all the values that make $(x + 3) (x - 3) = 0$ true.

$x = - 3, 3$