Precalculus Examples

$x (x^{2} - 6 x + 9) = 0$

Step 1

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

$x = 0$

$x^{2} - 6 x + 9 = 0$

Step 2

Set $x$ equal to $0$ .

$x = 0$

Step 3

Set $x^{2} - 6 x + 9$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $x^{2} - 6 x + 9$ equal to $0$ .

$x^{2} - 6 x + 9 = 0$

Step 3.2

Solve $x^{2} - 6 x + 9 = 0$ for $x$ .

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Step 3.2.1

Factor using the perfect square rule.

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Step 3.2.1.1

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

$x^{2} - 6 x + 3^{2} = 0$

Step 3.2.1.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$6 x = 2 \cdot x \cdot 3$

Step 3.2.1.3

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 3 + 3^{2} = 0$

Step 3.2.1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 3$ .

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

Step 3.2.2

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

$x - 3 = 0$

Step 3.2.3

Add $3$ to both sides of the equation.

$x = 3$

Step 4

The final solution is all the values that make $x (x^{2} - 6 x + 9) = 0$ true.

$x = 0, 3$